Thank you!
I maybe found something, but it is unfortunately completely unrelated to the plugin. If I open the wordpress core ajax handler file, then it should always print a ‘0’ character to the browser output. In your case however, if I keep refreshing the page a few times, I get nothing: https://i.imgur.com/CHsiQlX.png
This of course happens even if our plugin is disabled.
That is why the plugin reports an empty response message, as something is clearing the ajax output. I checked the PHP configuration, and the only thing that I think could cause this is the memcached PHP module. It is very rare to see memcached enabled, that is why I noticed. I recommend trying to uninstall that module via SSH to see if it makes any difference.