Lack of Freewill doesn't mean lack of choice

No, it’s the only real problem there is—every other problem is spurious. The general charge is that the notion is incoherent (arguments about determinism, causality, chance, and so on, and in particular the consequence argument, really are beside the point). The idea is that free will would be both ‘determinate and non-determined’, as I think you put it—i.e. there’s nothing that determines it, but it’s still supposed to have some determinate content. But this can only be coherent if it must be something beside the will that determines it—the will self-determining would not preclude its freedom. If it’s causa sui, then my will and nothing beside my will determines my actions. So such self-determination must be impossible. But this it only is if the regress entailed by self-determination is impossible. If it’s not, then the will determines itself, and is thereby free.

Our experience of our actions as free is the reason we posit the existence of free will. Any alternative then has the added explanatory burden of producing a reason for this illusory experience.

I have, at several points in this thread. For example:

More explicitly, there’s actually the same infinitary issue at work at every instance where some A causes B to occur:

(This thread-jumping is very awkward, by the way; so I’d propose that we keep matters regarding free will in this thread, leaving the other to Thomson’s lamp proper.)