I'm making the assumption that we've verified the predictor's accuracy, so it doesn't really matter how the predictor achieves it.

Right, and I'm saying that that assumption only holds in fiction, and so using decision procedures based on it is irrational.

In any case, this basically boils down to cause-and-effect once again: if you believe in "free will", then you'll object to the existence of a Predictor, and base your decisions accordingly. If you believe, however, in cause-and-effect, then a Predictor is at least theoretically possible.

I'm afraid this is a straw man - I'm with Dennett on free will. However, in most situations you find yourself in, believing that a Predictor has the aforementioned power is bad for you, free will or no.

Also, I'm not sure what you mean by 'at least theoretically possible'. Do you mean 'possible or not possible'? Or 'not yet provably impossible'? The Predictor is at best unlikely, and might be physically impossible even in a completely deterministic universe (entirely due to practicality / engineering concerns / the amount of matter in the universe / the amount that one has to model).

(By the way, if humans have free will -- i.e., the ability to behave in an acausal manner -- then so do subatomic particles.)

This does not logically follow. Insert missing premises?