Reposition post share buttons

Hi,
Sorry for the late reply and thanks for the mockup and link, so for your single posts we will first change the social share buttons into small buttons.
Please try this code in the General Styling > Quick CSS field or in the WordPress > Customize > Additional CSS field:

#top.single-post .av-share-box .avia-related-tooltip,
#top.single-post .av-share-box h5.av-share-link-description.av-no-toc {
  display: none !important;
}
#top.single-post .av-share-box {
    width: 200px !important;
    margin-top: 0 !important;
    margin-bottom: 0 !important;
    position: absolute;
    right: 50px;
}

#top.single-post .av-share-box .av-share-box ul li {    
    border-left-style: none;    
    display: inline-block;
}

#top.single-post .av-share-box .av-share-link {
   width: 30px!important;
   height: 30px!important;
   margin: 0 10px 0 0;    
}

#top.single-post .av-share-box .av-share-link a {   
   border:0px solid #000;
   padding: 0;
}

#top.single-post .av-share-box .av-share-link a:hover {
  background-color: #000!important;
  transition: all .35s ease;
}

#top.single-post .av-share-box .av-share-link a:before {
  color:#333;
  transition: all .5s ease;

}

#top.single-post .av-share-box .av-share-link:hover a:before {
  color:#fff;
  transition: all .35s ease;
}

Then we will move it to under your featured image, try adding this code to the end of your functions.php file in Appearance > Editor:

function custom_script() { ?>
    <script>
(function($) {
  $(document).ready(function(){
     $('.single-post .av-share-box').detach().insertBefore('.blog-meta');
  });
 })(jQuery);
</script>
    <?php
}
add_action('wp_footer', 'custom_script');

Then clear your browser cache and check.

Best regards,
Mike