To which I say: Given the two worlds and the otherwise identical twins populating them, what makes you think they are the zombies?
I one-box, but not because I haven't considered the two-box issue.
I one-box because it's a win-win in the larger context. Either I walk off with a million dollars, OR I become the first person to outthink Omega and provide new data to those who are following Omega's exploits.
Even without thinking outside the problem, Omega is a game-breaker. We do not, in the problem as stated, have any information on Omega other than that they are superintelligent and may be able to act outside of casuality. Or else Omega is simply a superduperpredictor, to the point where (quantum interactions and chaos theory aside) all Omega-chosen humans have turned out to be correctly predictable in this one aspect.
Perhaps Omega is deliberately NOT chosing to test humans it can't predict. Or it is able to affect the local spacetime sufficiently to 'lock in' a choice even after it's physically left the area?
We can't tell. It's superintelligent. It's not playing on our field. It's potentially an external source of metalogic. The rules go out the window.
In short, the problem as described is not sufficiently constrained to presume a paradox, because it's not confining itself to a single logic system. It's like asking someone only familiar with non-imaginary numbers what the square root of negative one is. Just because they can't derive an answer doesn't mean you don't have one - you're using different number fields.