It would become a mind game: you'd have to explicitly model how you think Omega is making the decision.

The problem you're facing is to maximise P(Omega rewards you|all your behaviour that Omega can observe). In the classical problem you can substitute the actual choice of one-boxing or two-boxing for the 'all your behaviour' part, because Omega is always right. But in the 'imperfect Omega' case you can't.