I'm not a big BASIC fan, so I've done my stuff in C, since it was a Motorola 68k on the TI-Voyage 200. I don't remember exactly how (it's 15+ year ago), but you could mark your app as a "system app" which was not removed during a factory reset.

Add a cryptic name, blank screen on start with a short timeout to return to menu when a key combination is not pressed and nobody will ever notice.