My CDT solution is to notice that Omega's promise of the future is correct, then it must be capable of bringing it about. Perhaps it knows how to teleport the larger reward away if we go for the visible reward. Maybe Omega is just a master stage magician. Point is, taking the action of going and getting the visible reward will prevent me from getting the invisible one. I don't need to worry about implementation details like whether it's really based on my decision before I make it, or just the actions I take after I make it. The constraint is equally real whether I understand the mechanism or not.

Yes, that dodges the real question, but can an example illustrating the same deficiency of CDT be constructed, that isn't subject to this dodge? I'm not certain it's possible.