I don't see that the scenario is the same. If you one-box everytime in your thought experiment, you are guaranteed to get the million; if you two box everytime, you will certainly not get the million. With Omega, there is a high probability but not certainty.
Also, what you do in the first round causes what happens in the second round, but with Omega, it is debatable whether what you end up doing causes there to be a million dollars or not.
You won't one-box every time. There is always some chance, however small, that you will two-box, and vice versa.
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.