Here's an example of a related kind of "reflexivity makes prediction meaningless". Let's say Omega bets you $100 that she can predict what you will eat for breakfast. Once you accept this bet, you now try to think of something that you would never otherwise think to eat for breakfast, in order to win the bet. The fact that your actions and the prediction of your actions have been connected in this way by the bet makes your actions unpredictable.

Your actions have been determined in part by the bet that Omega has made with you - I do not see how that is supposed to make them unpredictable any more than adding any other variable would do so. Remember: You only appear to have free will from within the algorithm, you may decide to think of something you'd never otherwise think about but Omega is advanced enough to model you down to the most basic level - it can predict your more complex behaviours based upon the combination of far simpler rules. You cannot necessarily just decide to think of something random which would be required in order to be unpredictable.

Similarly, the whole question of whether you should choose to two box or one box is a bit iffy. Strictly speaking there's no SHOULD about it. You will one box or you will two box. The question phrased as a should question - as a choice - is meaningless unless you're treating choice as a high-level abstraction of lower level rules; and if you do that, then the difficult disappears - just as you don't ask a rock whether it should or shouldn't crush someone when it falls down a hill.

Meaningfully, we might ask whether it is preferable to be the type of person who two boxes or the type of person who one boxes. As it turns out it seems to be more preferable to one-box and make stinking great piles of dosh. And as it turns out I'm the sort of person who, holding a desire for filthy lucre, will do so.

It's really difficult to side step your intuitions - your illusion that you actually get a free choice here. And I think the phrasing of the problem and its answers themselves have a lot to do with that. I think if you think that people get a choice - and the mechanisms of Omega's prediction hinge upon you being strongly determined - then the question just ceases to make sense. And you've got to jettison one of the two; either Omega's prediction ability or your ability to make a choice in the sense conventionally meant.