We would have to test the speed to see what the extra network would add…
I'm not sure about a reliability difference as if you don't also have the web server then the PHP scripts alone won't be and it seems that you would be adding another point of failure unless you can automaticaly share all PHP processes between both servers.
The first thing we would move would by MySQL to create a multiple server cluster. We've alread clustered DNS servers but that doesn't use much ressources.
The server we're currently trying to get running smoothly with litespeed has more than 5 times CPU than our previous server and 10 times more memory so with the right software and settings we should be able to hold out quite some time on the new server configuration.
If you're using a NAS for the files, why not go the whole way with a load balancer ?