Thank you for the insightful responses. I’ll be looking into everything that’s been mentioned here. One point I’d like to clarify, though, is that in the protocol I’m working on, private key collisions are expected to be a regular occurrence. I understand this might seem unconventional.
If your private keys are expected to collide, then you need a second private key that can't collide and would determine the owner in case of a collision. Or how about 2-of-2 multisig?