Ok, I was able to resolve the issue by overriding the set_default_values function in the shortcode class.
I added the function from enfold/config-templatebuilder/avia-template-builder/php/shortcode-template.class.php

/**
		 * helper function executed by aviaShortcodeTemplate::popup_editor that extracts the attributes from the shortcode and then merges the values into the options array
		 *
		 * @param array $elements
		 * @return array $elements
		 */
		public function set_default_values($elements)
		{
			$shortcode = !empty($_POST['params']['shortcode']) ? $_POST['params']['shortcode'] : '';
			

			if($shortcode)
			{
				//will extract the shortcode into $_POST['extracted_shortcode']
				$this->builder->text_to_interface($shortcode);
				
				//the main shortcode (which is always the last array item) will be stored in $extracted_shortcode
				$extracted_shortcode = end($_POST['extracted_shortcode']);

				//if the $_POST['extracted_shortcode'] has more than one items we are dealing with nested shortcodes
				$multi_content = count($_POST['extracted_shortcode']);

				//proceed if the main shortcode has either arguments or content
				if(!empty($extracted_shortcode['attr']) || !empty($extracted_shortcode['content']))
				{
					if(empty($extracted_shortcode['attr'])) $extracted_shortcode['attr'] = array();
					if(isset($extracted_shortcode['content'])) $extracted_shortcode['attr']['content'] = $extracted_shortcode['content'];

					//iterate over each array item and check if we already got a value
					foreach($elements as &$element)
					{
						if(isset($element['id']) && isset($extracted_shortcode['attr'][$element['id']]))
						{
							//make sure that each element of the popup can access the other values of the shortcode. necessary for hidden elements
							$element['shortcode_data'] = $extracted_shortcode['attr'];
						
							//if the item has subelements the std value has to be an array
							if(isset($element['subelements']))
							{
								$element['std'] = array();

								for ($i = 0; $i < $multi_content - 1; $i++)
								{
									$element['std'][$i] = $_POST['extracted_shortcode'][$i]['attr'];
									$element['std'][$i]['content'] = $_POST['extracted_shortcode'][$i]['content'];
								}
							}
							else
							{
								$element['std'] = stripslashes($extracted_shortcode['attr'][$element['id']]);
							}

						}
						else
						{
							if($element['type'] == "checkbox") $element['std'] = '';
						}
					}
				}
			}

			return $elements;
		}

I modified it to be as follows:

    /**
     * helper function executed by aviaShortcodeTemplate::popup_editor that extracts the attributes from the shortcode and then merges the values into the options array
     *
     * @param array $elements
     * @return array $elements
     */
    public function set_default_values($elements)
    {
      $shortcode = !empty($_POST['params']['shortcode']) ? $_POST['params']['shortcode'] : '';
      

      if($shortcode)
      {
        //will extract the shortcode into $_POST['extracted_shortcode']
        $this->builder->text_to_interface($shortcode);
        
        //the main shortcode (which is always the last array item) will be stored in $extracted_shortcode
        $extracted_shortcode = end($_POST['extracted_shortcode']);

        //if the $_POST['extracted_shortcode'] has more than one items we are dealing with nested shortcodes
        $multi_content = count($_POST['extracted_shortcode']);

        //proceed if the main shortcode has either arguments or content
        if(!empty($extracted_shortcode['attr']) || !empty($extracted_shortcode['content']))
        {
          if(empty($extracted_shortcode['attr'])) $extracted_shortcode['attr'] = array();
          if(isset($extracted_shortcode['content'])) $extracted_shortcode['attr']['content'] = $extracted_shortcode['content'];

          //iterate over each array item and check if we already got a value
          foreach($elements as &$element)
          {
            if(isset($element['id']) && isset($extracted_shortcode['attr'][$element['id']]))
            {
              //make sure that each element of the popup can access the other values of the shortcode. necessary for hidden elements
              $element['shortcode_data'] = $extracted_shortcode['attr'];
            
              //if the item has subelements the std value has to be an array
              if(isset($element['subelements']))
              {
                $element['std'] = array();

                for ($i = 0; $i < $multi_content - 1; $i++)
                {
                  $element['std'][$i] = $_POST['extracted_shortcode'][$i]['attr'];
                  $element['std'][$i]['content'] = $_POST['extracted_shortcode'][$i]['content'];
                }
              }
              else
              {
                $element['std'] = html_entity_decode(stripslashes($extracted_shortcode['attr'][$element['id']]));
              }

            }
            else
            {
              if($element['type'] == "checkbox") $element['std'] = '';
            }
          }
        }
      }

      return $elements;
    }

The difference is that I changed this:
$element['std'] = stripslashes($extracted_shortcode['attr'][$element['id']]);
to this:
$element['std'] = html_entity_decode(stripslashes($extracted_shortcode['attr'][$element['id']]));

and included it in my shortcode element, which is finished below:

<?php
/**
 * 2 Column Module
 * 
 * Builds 2 column modules with image on one side and content on the other.
 */
if ( ! defined( 'ABSPATH' ) ) {  exit;  }    // Exit if accessed directly

if ( ! class_exists( 'avia_sc_two_column_module' ) )
{
  class avia_sc_two_column_module extends aviaShortcodeTemplate
  {
    /**
     * Create the config array for the shortcode button
     */
    function shortcode_insert_button()
    {
      $this->config['version']    = '1.0';
      $this->config['self_closing'] = 'yes';

      $this->config['name']   = __( '2 Column Modules', 'avia_framework' );
      $this->config['tab']    = __( 'Content Elements', 'avia_framework' );
      $this->config['icon']   = AviaBuilder::$path['imagesURL'] . 'sc-blog.png';
      $this->config['order']    = 40;
      $this->config['target']   = 'avia-target-insert';
      $this->config['shortcode']  = 'av_two_column_module';
      $this->config['tooltip']  = __( 'Builds 2 Column Modules ', 'avia_framework' );
      $this->config['preview']  = false;
      $this->config['id_name']  = 'id';
      $this->config['id_show']  = 'yes';
      $this->config['alb_desc_id']  = 'alb_description';
    }

    function admin_assets()
    {
      $ver = AviaBuilder::VERSION;
     
    }

    function extra_assets()
    {
      wp_enqueue_style( 'two-column-module', get_stylesheet_directory_uri() . '/shortcodes/assets/twocolumnmodule.css', array( 'avia-layout' ), false );
    }

    /**
     * helper function executed by aviaShortcodeTemplate::popup_editor that extracts the attributes from the shortcode and then merges the values into the options array
     *
     * @param array $elements
     * @return array $elements
     */
    public function set_default_values($elements)
    {
      $shortcode = !empty($_POST['params']['shortcode']) ? $_POST['params']['shortcode'] : '';
      

      if($shortcode)
      {
        //will extract the shortcode into $_POST['extracted_shortcode']
        $this->builder->text_to_interface($shortcode);
        
        //the main shortcode (which is always the last array item) will be stored in $extracted_shortcode
        $extracted_shortcode = end($_POST['extracted_shortcode']);

        //if the $_POST['extracted_shortcode'] has more than one items we are dealing with nested shortcodes
        $multi_content = count($_POST['extracted_shortcode']);

        //proceed if the main shortcode has either arguments or content
        if(!empty($extracted_shortcode['attr']) || !empty($extracted_shortcode['content']))
        {
          if(empty($extracted_shortcode['attr'])) $extracted_shortcode['attr'] = array();
          if(isset($extracted_shortcode['content'])) $extracted_shortcode['attr']['content'] = $extracted_shortcode['content'];

          //iterate over each array item and check if we already got a value
          foreach($elements as &$element)
          {
            if(isset($element['id']) && isset($extracted_shortcode['attr'][$element['id']]))
            {
              //make sure that each element of the popup can access the other values of the shortcode. necessary for hidden elements
              $element['shortcode_data'] = $extracted_shortcode['attr'];
            
              //if the item has subelements the std value has to be an array
              if(isset($element['subelements']))
              {
                $element['std'] = array();

                for ($i = 0; $i < $multi_content - 1; $i++)
                {
                  $element['std'][$i] = $_POST['extracted_shortcode'][$i]['attr'];
                  $element['std'][$i]['content'] = $_POST['extracted_shortcode'][$i]['content'];
                }
              }
              else
              {
                $element['std'] = html_entity_decode(stripslashes($extracted_shortcode['attr'][$element['id']]));
              }

            }
            else
            {
              if($element['type'] == "checkbox") $element['std'] = '';
            }
          }
        }
      }

      return $elements;
    }
    /**
     * Popup Elements
     *
     * If this function is defined in a child class the element automatically gets an edit button, that, when pressed
     * opens a modal window that allows to edit the element properties
     *
     * @return void
     */
    function popup_elements()
    {      
      
      $this->elements = array(
          
        array(
            'type'  => 'tab_container', 
            'nodescription' => true
          ),
            
        array(
            'type'  => 'tab',
            'name'  => __( 'Content', 'avia_framework' ),
            'nodescription' => true
          ),
        array(
              'type'      => 'template',
              'template_id' => 'toggle_container',
              'templates_include' => array(
                          $this->popup_key( 'selected_project' )
                        ),
              'nodescription' => true
            ),
        
        array(
            'type'  => 'tab_close',
            'nodescription' => true
          ),
         
        array(
            'type'  => 'tab',
            'name'  => __( 'Advanced', 'avia_framework' ),
            'nodescription' => true
          ),
        
          array(
              'type'  => 'toggle_container',
              'nodescription' => true
            ),
        
            array(  
                'type'      => 'template',
                'template_id' => 'screen_options_toggle'
              ),
        
            array(  
                'type'      => 'template',
                'template_id' => 'developer_options_toggle',
                'args'      => array( 'sc' => $this )
              ),
        
          array(
              'type'  => 'toggle_container_close',
              'nodescription' => true
            ),
        
        array(
            'type'  => 'tab_close',
            'nodescription' => true
          ),

        array(
            'type'  => 'tab_container_close',
            'nodescription' => true
          )

          
          
        );

    }
    
    /**
     * Create and register templates for easier maintainance
     * 
     * @since 4.6.4
     */
    protected function register_dynamic_templates()
    {
      
      /**
       * Content Tab
       * ===========
       */
      
      $c = array(
            array(
              'name'  => __( 'Module Content', 'avia_framework' ),
              'desc'  => __( 'What is the content for this module?', 'avia_framework' ),
              'id'    => 'module_content',
              'type'  => 'tiny_mce',
              'std'   => '',
            ),
            array(
              'name'  => __( 'Module Image', 'avia_framework' ),
              'desc'  => __( 'What is image for this module? (Select Large if available, Full Size if Large is not available.)', 'avia_framework' ),
              'id'  => 'module_image',
              'type'  => 'image',
              'title' => __( 'Insert Image', 'avia_framework' ),
              'button'  => __( 'Insert', 'avia_framework' ),
              'std' => AviaBuilder::$path['imagesURL'] . 'placeholder.jpg' 
            ),
            array(
              'name'  => __( 'Image Side?', 'avia_framework' ),
              'desc'  => __( 'What side of the module will the image be on?', 'avia_framework' ),
              'id'  => 'image_side',
              'type'  => 'select',
              'std'   => 'left',
              'subtype' => array(
                        __( 'Left', 'avia_framework' ) => 'left',
                        __( 'Right', 'avia_framework' )  => 'right'
                      )
            )
        );
      
      $template = array(
              array(  
                'type'      => 'template',
                'template_id' => 'toggle',
                'title'     => __( '2 Column Module', 'avia_framework' ),
                'content'   => $c 
              ),
          );
      
      AviaPopupTemplates()->register_dynamic_template( $this->popup_key( 'selected_project' ), $template );
      
    }
    /**
     * Editor Element - this function defines the visual appearance of an element on the AviaBuilder Canvas
     * Most common usage is to define some markup in the $params['innerHtml'] which is then inserted into the drag and drop container
     * Less often used: $params['data'] to add data attributes, $params['class'] to modify the className
     *
     *
     * @param array $params this array holds the default values for $content and $args.
     * @return $params the return array usually holds an innerHtml key that holds item specific markup.
     */
    function editor_element( $params )
    {

      $params = parent::editor_element( $params );
      $params['content'] = null; //remove to allow content elements

      return $params;
    }

    /**
     * Frontend Shortcode Handler
     *
     * @param array $atts array of attributes
     * @param string $content text within enclosing form of shortcode element
     * @param string $shortcodename the shortcode found, when == callback name
     * @return string $output returns the modified html string
     */
    function shortcode_handler( $atts, $content = '', $shortcodename = '', $meta = '' )
    {
      global $avia_config, $more;

      extract( $atts );

      $cards = [];
      
      ob_start(); //start buffering the output instead of echoing it
      $img = wp_get_attachment_image( $attachment, 'large' );
      echo $this->render_module(ShortcodeHelper::avia_apply_autop( ShortcodeHelper::avia_remove_autop( $module_content ) ), $image_side, $module_image, $img);
      $output = ob_get_clean();
      
      avia_set_layout_array();

      return $output;
    }

    function render_module($content,$image_side,$module_image, $image) {
      $html = '';
      $html .= '<div class="two-column-module '.$image_side.'-side">';
      $html .= '<div class="image-container"><div class="module-image" style="background:url(\''.$module_image.'\'); background-repeat: no-repeat; background-position: center '.$image_side.'; background-size: cover"></div></div>';
      $html .= '<div class="content-container">'.$content.'</div>';
    return $html .= '</div>';
    }

   }
  
}

It also works properly with multiple tiny_mce boxes, too.
Note – this is only a problem when you create a custom shortcode element and give it an id of something other than ‘content’.

I was able to fix the issue, although I had to hard-code it into the theme file, which I hate doing.

I added the below code to the enfold/config-templatebuilder/avia-template-builder/php/html-helper-class.php file.
$element['std'] = html_entity_decode($element['std']);

You can put it anywhere within the tiny_mce function.

static public function tiny_mce($element)
		{
			//tinymce only allows ids in the range of [a-z] so we need to filter them. 
			$element['id']  = preg_replace('![^a-zA-Z_]!', '', $element['id']);
			
			
			/* monitor this: seems only ajax elements need the replacement */
			$user_ID = get_current_user_id();
			
			if(get_user_meta($user_ID, 'rich_editing', true) == "true" && isset($element['ajax']))
			{
				global $wp_version;
				
				//replace new lines with brs, otherwise the editor will mess up. this was fixed with wp 4.3 so only do that in old versions
				if ( version_compare( $wp_version, "4.3", '<' ) ) 
				{
					$element['std'] = str_replace("\n",'<br>',$element['std']);
				}
			}
			
			$element['std'] = html_entity_decode($element['std']);
			
			ob_start();
	        wp_editor( $element['std'], $element['id'] , array('editor_class' => 'avia_advanced_textarea avia_tinymce', 'media_buttons' => true ) );
	        $output = ob_get_clean();
	        
	        return $output;
		}

I haven’t yet found a place where I can override what gets passed into this function as the $element argument, in order to avoid hard-coding it into the file.

Since I’ve gotten it this far, would it be possible for somebody on the team to possibly figure out how to finish resolving the issue, without having to hard-code it into the theme file?

BTW the W3TCache plugin doesn’t change the rest of your htaccess. The reason why I am saying is that in the htaccess, I have manually specified some minification settings etc. So it makes sense that enabling/disabling this from within Enfold or W3TC won’t make a difference. Anyway, I manually purged Redis & Varnish but this doesn’t seem to make a difference.

Can’t we specify something in the Quick CSS settings to verify that this pushed through (or not)?
When I update a page, these changes are visible. I.e. on the homepage, I updated a button and the change is displayed correctly.

Cheers,
Dimitri