You're presenting a standard PD, only distributed across possible worlds. Doesn't seem to be any difference between splitting into 2 possible worlds, and taking 2 prisoners into 2 different cells. So you would need to provide a solution, a mechanism for cooperation, that would also work for the PD. And you haven't.

Don't know what you mean by "accept counterfactual mugging". Especially since I just said I don't agree with your interpretation of it. I believe the counterfactual mugging is also just a rephrasing of the PD. You should keep the $100 unless you would cooperate in a one-shot PD. We all know that rational agents would do better by cooperating, but that doesn't make it happen.