This is just a bit of feedback which might be fixable, and if not, might save someone some time.
I was trying to host a "PHP-FPM+Nginx" application as a subdirectory on the same domain as one of my Wordpress sites. Unfortunately, any attempt to access that application would return a 404 error from Apache.
I created a new application, this time a plain "PHP+Apache" one, and copied all the same PHP files in, and routed the subdirectory to this application instead of the old one - and now it works.
I suspect there's some sort of incompatibility between Nginx and Apache both trying to handle the same domain? Perhaps the route gets set in the Nginx configuration to the Nginx application, but the request actually goes via Apache because that handles the application at the domain's URI root?