Oh, and Parfit's Hitchhiker highlights that the concept of honor is a layman's version of reflective consistency: you tell the driver that you are a (wo)man of your word, because you truly are, for decision-theoretical reasons, as well as because you were brought up this way.

So, my hypothesis predicts that theists will not do better on "Newcomblike problems" not involving deities.

I've always had trouble with this part. I went through the reasoning that Newcomb is two PDs side by side, but this side-by-sideness seems to kill the essential part of PD, its unpredictability. Newcomb is perfectly deterministic, whereas in PD you depend on what the other party will do and often hope that they are reflectively consistent. The one-shot counterfactual mugging is again different from one-shot PD, even if one is reflectively consistent.