finding new forum software that is compatible with php/phpBB (which I assume ours is)
I think that this is part of the problem. We run SMF (Simple Machines), which from what I understand isn't easily compatible with phpBB.
Then, before byennie took over, several tech guys that didn't completely know what they were doing, attempted various fixes, which didn't necessarily help.
A transition from SMF to a different bulletin board system is probably possible, but it would take somebody with SMF experience.