In this case, if your pre-prior is consistent and reasonable, but doesn't satisfy the pre-rationality condition relative to your prior, the obvious plan is to update your prior to be whatever the pre-rationality condition says it should be (treating prior "P" as just a label).

That doesn't seem to work in the specific example I gave. If the "optimistic" AI updates its prior to be whatever the pre-rationality condition says it should be, it will just get back the same prior O, because according to its pre-prior (denoted r in my example), it's actual prior O is just fine, and the reason it's not pre-rational is that in the counterfactual case where the B coin landed tails, it would have gotten assigned the prior P.

Or am I misinterpreting your proposed solution? (ETA: Can you make your solution formal?)