The logical/physical distinction itself can be seen as ad-hoc: you can consider the whole set-up Q as a program that is known to you (R), because the rules of the game were explained, and also consider yourself (R) as a program known to Q. Then, Q can reason about R in interaction with various situations (that is, run, given R, but R is given as part of Q, so "given R" doesn't say anything about Q), and R can do the same with Q (and with the R within that Q, etc.). Prisoner's dilemma can also be represented in this way, even though nobody is pulling Omega in that case.

When R is considering "the past", it in fact considers facts about Q, which is known to R, and so facts about the past can be treated as "logical facts". Similarly, when these facts within Q reach R at present and interact with it, they are no more "physical facts" than anything else in this setting (these interactions with R "directed from the past" can be seen as what R predicts Q-within-R-within-Q-... to do with R-within-Q-within-R-...).

This ad-hoc fix breaks as soon as Omega makes a slightly messier game, wherein you receive a physical clue as to a computation output, and this computation and your decision determine your reward.

Suppose that for any output of the computation there is a a unique best decision, and that furthermore this set of (computation output, predicted decision) pairs are mapped to distinct physical clues. Then given the clue you can infer what decision to make and the logical computation, but this requires that you infer from a logical fact (the predictor of you) to the physical state to the clue to the logical fact of the computation.