What I mean is that no one has provided a reductionist account of how the naive notion of free will could work.

Because that would be as silly as seeking a reductionist account of how souls or gods could "work" -- the only way you're going to get one is by explaining how the brain tends to believe these (purely mental) phenomena actually exist.

Free will is just the feeling that more than one choice is possible, just like a soul or a god is just the feeling of agency, detached from an actual agent.

All three are descriptions of mental phenomena, rather than having anything to do with a physical reality outside the brain.