So instead of trying your solution I dug a bit deeper, and I may have solved your problem. I remembered that I returned an HTTP error on a large image file upload. I researched that problem, and researched this problem and found an odd solution.
I wiped the database and did a clean install of wordpress, clean install of enfold, and made some custom modifications to files via cpanel.

In my public HTML in the .htaccess file I added:
SetEnv MAGICK_THREAD_LIMIT 1
I added this code to the top of the file.
I also added the following code to the bottom of the file:
suphp_configpath /home/genesysg/public_html/
# Exclude the file upload and WP CRON scripts from authentication
<FilesMatch “(async-upload\.php|wp-cron\.php|xmlrpc\.php)$”>
Satisfy Any
Order allow,deny
Allow from all
Deny from none
</FilesMatch>
In the public HTML folder I created a file called php.ini and added the following code:
display_errors = On;
memory_limit = 512M;
In the WP ADMIN directory I created a .htaccess file and added the following code:
<IfModule mod_security.c>
SecFilterEngine Off
SecFilterScanPOST Off
</IfModule>
I tried adding the following code to the php.ini and .htaccess files in the public html but was met with an internal server 500 error.
upload_max_filesize = 64M
post_max_size = 64M
max_execution_time = 300
I deleted the code from both files and the site was back up. I don’t know if the error was due to redundant code or if I would have to ask my hosting provider to increase my limit.

Once the site was back up I used my API key to activate the them and tried the one-click demo upload one more time. The process worked for several minutes, much longer than before, and then returned the error that it in fact did not work. (Demo importing didn’t work, try refreshing the browser) I checked the media folder and many more pictures had successfully imported whereas in the past only a few had successfully imported. I checked the site to see what it looked like and I have a fully functioning demo installation installed. I haven’t gotten a chance to look at it fully but it appears even though it returned an error saying that it did not work, it did install the demo content.

The login and password is in the hidden data. Please check the site and let me know what you think about my workaround and why you imagine it produced the same error even though the import was successful. Am I missing any important files or pieces?