Free will is not a necessary component of QM. So I certainly am not rejecting superdeterminism because of that. I reject superdeterminism as an explanation for Bell test results, and I do so for the reasons already stated.
Please bear in mind that there are no candidate superdeterministic theories to reject at this point, so it is a moot point in many ways. The reason I mention the amount of local information to be stored in every particle is because a candidate theory will end up postulating this (in some form or fashion) as a way to explain Bell test results. It is not necessary to assume free choice for measurement settings in any stage of the argument, but you must explain how (i.e. the exact mechanism, since we have no other reason to suspect it exists) the choice is propagated in a superdeterministic candidate.
Not so easy, I assure you. Which is again, the answer to your original question.