can you give some information about the tech stack which is in use? as mentioned in the other topic (which unfortunately has been closed) i am also admin of some sites with a couple of thousands users, even if people like @fenrirwulfcan not imagine that. maybe i can give some useful tips in regards to performance or in how to find the bottleneck.
thanks for your effort!
regarding your tasks: 1) i really dont think that there is a hardware upgrade required because it runs now, so if you did not change the hardware, it must be a software problem. 2) if its already running with php-fpm, i see no reason to switch except maybe consider using some caching (thats also one of the reasons i asked for the stack). if you run centos 7 i guess its php5. moving to php7 will absolutely improve performance, if the problem was a php problem. 4) i am very sure it was no problem with external resources because small snippets where loading very fast (png's etc.), but what was loading slow was everything related to .php
and again, thanks. i also work fulltime as java dev, i know how hard it is to have projects running parallel