I got back to the cabinet today and I set the exit hotkey to escape, and I was able to exit the game with the button on my control panel, but it still didn't close Dolphin. Alt-F4 was still required to close the Dolphin window. I did end up having to use xbindkeys and wmctrl to make it work. Perhaps the latest versions exit properly, but I'm using an old version that seems to run fastest on my old E8400@3.6GHz (5a77cae2e343). For anyone who's interested, I'm using Cabrio as my frontend, and it's working perfectly for the following emulators:
MAME
Stella
Mednafen
PCSX2
and now... Dolphin-emu
MAME
Stella
Mednafen
PCSX2
and now... Dolphin-emu