It turns it into a kind of prisoner's dilemma where all guards rebelling means everyone dies, while only some guards rebelling means the guards that rebelled die while everyone else (including the billionaire) get to live

It's incredibly unethical, but in a game theory sense it seems sound. Any one guard is punished for rebelling, and even if everyone coordinates they can't do anything about it. At least if you can eliminate the obvious weak points: the collars would have to be automatically activated