[Chris is me]

It's hard to recommend options that don't backdrive without knowing your application, since it really does vary. If it's a winch and release mechanism, like a spring loaded shooter, it can be as simple as throwing a Craftsman wrench on one of your hex shafts for a makeshift ratchet. This is more difficult if your mechanism needs to be powered in more than one direction, obviously, but it's one simple solution.

Does it need to hold position when the robot is disabled? If it isn't a scaling mechanism I don't see why it would. Things like arms can, if well designed, be lightly stalled in order to hold position for short durations. You don't necessarily need a mechanical brake for these to work.

You could also modify old window motors you already have. I know of a team that plugged a BAG motor into a window motor gearbox for an anti-backdrive mechanism.