Okay, here are some options for this...
Have the keyboard accessible. :-) (The ArcadePC has a keyboard drawer, so you could just pull it out. But this ruins the illusion of being a pure arcade machine.)
Tell folks to use the upper-middle player 1 button (sends an Alt). This will put you in menu mode for most windows programs. Use the joystick down to navigate down to 'exit'.
Get an auxiliary programmable keypad, and map a button to ALT-F4. That exits most programs.
At the windows level, remap the "second" credit button so what it sends ('4') is interpreted as TAB. (Remapping software is linked here.) Then use the abovementioned 'Alt' key + this key -- this gives you an ALT-TAB windows task switch command. If no other programs are running (which is logical in "arcade only" mode), then ALT-TAB will wake up PartyOn. PartyOn has been programmed to kill off whatever program it started when it's awakened, so you're all set. Yes, this is ugly, but it's how we have it set up, and it works just great.