The rationale for two-boxing that Nozick describes in the original paper has nothing to do with the predictor being wrong. It says that even if the predictor is right, you should still two-box.
Omega has already put either $1M or $0 in Box B. It’s sitting right there.
If Omega put $1M, then I can one-box for $1M or two-box for $1M + $1,000. Therefore I should two-box.
If Omega put $0, then I can one-box for $0 or two-box for $0 + $1,000. Therefore I should two-box.
The point isn’t that Omega is a faulty predictor. The point is that even if Omega is an awesome predictor, then what you do now can’t magically fill or empty box B. Two-boxers of this type would love to precommit to one-boxing ahead of time, since that would causally change Omega’s prediction. They just don’t think it’s rational to one-box after the prediction has already been made.
Maybe I’m just rehashing what you said in your edit :) In any case, I think that is the most sympathetic argument for two-boxing if you take the premise seriously. I still think it’s wrong (I’m a dedicated one-boxer), but I don’t think the error is believing that the predictor is mistaken.
In the same survey, decision theorists are as convinced of compatibilism as they are of two-boxing:
https://survey2020.philpeople.org/survey/results/4838?aos=1399
Compatibilism would hold that Omega can indeed be a perfect or near-perfect predictor. For those unfamiliar, compatibilism is the belief that we live in a determinstic world, but that doesn’t mean that we aren’t free. For instance, classical compatibilism holds that “freedom is nothing more than an agent’s ability to do what she wishes in the absence of impediments that would otherwise stand in her way,” (source) even if what an agent wishes is entirely causally determined by the physics in her brain. Even determinists can accept that agents can do things that they want to do!
The sort of free will that implies independence from a predictor would be “libertarian” free will, which only 4% of decision theorists believe in. That 4% cannot explain the overwhelming majority in favor of two-boxing.