Thanks for your answer! First, since it's been a while since I posted this: I'm not sure my reasoning in this post is correct, but it does still seem right to me. I'd now gloss it as, in a Counterfactual Mugging there really is a difference as to the best course of action given your information yesterday and your information today. Yes, acting time-inconsistently is bad, so by all means, do decide to be a timeless decider; but this does not make paying up ideal given what you know today, choosing according to yesterday's knowledge is just the best of the bad alternatives. (Choosing according to what a counterfactual you would have known a million years ago, OTOH, does not seem the best of the bad alternatives.)

That said, to answer your question -- if we can assume for the purpose of the thought experiment that we know the source code of the universe, what would seem natural to me would be to program UDT's "mathematical intuition module" to assign low probability to the proposition that this source code would output a purple Alpha Centauri.

Which is -- well -- a little fuzzy, I admit, because we don't know how the mathematical intuition module is supposed to work, and it's not obvious what it should mean to tell it that a certain proposition (as opposed to a complete theory) should have low probability. But if we can let logical inference and "P is false" stand in for probability and "P is improbable," we'd tell the AI "the universe program does NOT output a purple Alpha Centauri," and by simple logic the AI would conclude IsOdd(Pi(10^100)).