It's easy to construct a thought experiment with contradictory premises, and not notice if you keep math and pictures out of it. Draw pictures, show the math. It makes normal problems easier, and helps you notice when a problem boils down to "could an unstoppable force move an immovable object?", and then you can move on.

The unstoppable force being Omega's prediction ability, and the immovable object being causality only propagating forward in time. Two-boxers answer "unmovable object," one-boxers answer "unstoppable force."

I'm confused by what you mean here about Newcomb's problem, if you say that two-boxers and one-boxers are both failing to dissolve the question. Do you mean that one particular argument for two-boxing and one particular argument for one-boxing are failures to dissolve the question (but that one or the other decision is still valid)? Or do you mean that Newcomb's Problem is an impossible situation which doesn't approximate anything we might really face, and therefore we should stop worrying about it and move on? Or do you mean something different entirely?