I know if you hold P1 Start and then press P2 Start you will exit out, P1 Start acts like a Shift key of sorts. That's a Hyperspin shortcut and there are others such as P1 Start + P1 Down = Pause plus more I can't recall. There have been times where I've been playing a game with a mate and we've both gone to hit our start buttons to continue and BAM! Exited!
It might be worth having a poke around in Hyper HQ to find the shortcuts and see if there's one in there that might be messing with you.
I'm with you on the MAME only side of things, more than happy with just that. I find the SNES one can be buggy with arcade controls, I'll probably set that up on my PC with a gamepad at some point. As for setting up the Amiga emulator, I had it working once but never again. Another one for the PC methinks!
"If I can't build a time machine then I'll build machines from back in time." - Me