I haven't read Robin's paper. But this setup, and the difficulties you point out, remind me of the "centered" credulity functions that Nick Bostrom discusses in his Sleeping Beauty (SB) paper. (ETA: Here's a link to that paper.)

I haven't thought much about this, so maybe the similarity is superficial. Or I might be misremembering Bostrom's paper in some crucial way. But, as I recall, he gives one credulity function P to SB-before-she-learns-it's-Monday, but he gives another credulity function P+ to SB-after-she-learns-it's-Monday.

The key is that, in general, P+(X) does not equal P(X | MONDAY). That is, you don't get P+ by just using P and conditioning on MONDAY. This is the crucial ingredient that Bostrom uses to evade the usual paradoxes that arise when you naively apply Bayesianism to SB's situation.

Hanson's equation

P(A=heads) = r(A=heads | p=P)

seems analogous to forcing

P+(X) = P(X | MONDAY),

so I wonder if there is some analogy between the difficulties that forcing either one engenders.

ETA: . . . and hence an analogy between their solutions.