This is actually insightful, given that the most frequently proposed way for Omega to make predictions is to simulate the decision-maker - in which case you run into a Sleeping Beauty problem in which you are the real or simulated decision-maker.
I like this phrasing. It's less ambiguous.
I agree that this takes us into the world of Sleeping Beauty problems. But those are much harder. This makes things worse.
This is equivalent to Newcomb's Problem in the sense that any strategy does equally well on both, where by "strategy" I mean a mapping from info to (probability distributions over) actions.
I suspect that any problem with Omega can be transformed into an equivalent problem with amnesia instead of Omega.
Does CDT return the winning answer in such transformed problems?
Discuss.