Ok, more thoughts on the RR claim.
If RR actually has the princess card:
If RR is town:
guard-kill - If we guard kill town!RR, then we are in a 6v2 scenario and we lose with a mislynch. This will basically put us in another no-lynch scenario, and giving up two lynches in a game is not a good thing, but I think that is what we will have to do. 5v2, lylo.
lynch - Skip the guard-kill, but still lynch RR. It is basically the same as guard-killing RR, except we removed the option of no-lynch entirely. All this would do is make us feel better about not being forced into a no-lynch scenario. The one advantage of this is we don't expose a guard to a possible baron-kill.
leave alone completely - This is extremely dangerous. If we do this and mislynch we lose if scum has a guard/prince. A mislynch puts us at 5v2, scum kills town, then kills RR, 4v2 on D3, town loses. And I think we have to assume that scum have a card that can vig RR. Guard or prince both work as a vig card against princess and with 7 of those cards in the deck it is too likely that scum will have one of them for us to risk just leaving this alone.
If RR is scum:
Lynch over guard-kill for sure. The only reason he would claim princess as scum would be to reveal a guard for his partner to baron-kill.
If RR is fake-claiming princess
If RR is town:
This is actually a really interesting situation. Possibly very beneficial for us. If RR has some random card (not princess) and if RR is town, if we leave him alone there is the possibility that if we mislynch today, scum assumes they have the win in the bag with a guard-kill tomorrow, but instead it just outs scum. So beneficial. Except we are still at lylo.
If RR is scum:
We need to lynch him, obviously. But again, fake-claiming princess seems to be beneficial to scum in that it can possibly reveal a guard so that scum can baron-kill that person. An attempt to guard-kill scum here is not useful to us.
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So my conclusion after all this is that if RR is actually town and RR's claim is actually true, we are basically at lylo right now. I just don't see RR as being town when I look at it though. I mean, he was setting up this claim (true or false) back on D1. Yeah, I can see town!RR doing that, its just that I don't think that is what we have here.