In this case, I'd suggest making multi-button combinations mappable to bring up the menu. I don't want/need a dedicated MENU button anywhere. Set an option that disables the MENU, or base it on profiles. So I can have a kids profile, that disables anything to do with admin, for when the kids are playing.
When you have 10 kids, that can't/don't read anything, pounding on a control panel and will just click on anything... having any additional menus pop-up is a really bad idea.