Yet people see the practical question of whether the criminal is likely to commit the same crime again, as being in conflict with the "moral" question of whether the criminal had free will. If you have no free will, they say, you can do the wrong thing, and be moral; or you can do the right thing, and not be moral.

The only way this can make sense, is if morality does not mean doing the right thing.

"Moral" and "legal" mean different things anyway. It makes sense that someone did the legally wrong thing, but were not culpable. We regularly make such decisions where some is exonerated on grounds of being a minor, insane, etc. There is a link between legality and morality; if it is expressed as something like "illegal acts are those acts which are morally wrong when committed by a moral agent"

We only change our credit assignment due to a brain condition if we are trying to assign credit to the non-physical part of a person (their soul).

I don't see how that follows. If we believe that intentions and volitions exist, and have naturalistic roots in certain brain mechanisms, then their possessing a brain condition could affect our credit assignment. Naturalists can be libertarians too

It isn't parsimonious. It confuses the question of figuring out what values are good, and what behaviors are good, with the philosophical problem of free will. Each of these problems is difficult enough on its own!.

That is to beg the question against the idea that morality is in fact dependent on philosophical free will. The point remains that practical/legal ethics can and should be considered separately from philosophical free will (but not from practical FW of the kind removed by having a gun-pointed-at-your-head). However practical/legal/social ethics already are considered largely separately from the philosophical questions. It might be the case that the two constelations of issues are merged in the thinking of the general public. but that is not greatly impactful since actual law and philosophy are written by different groups of differently trained specialists.

they end up believing there are no objective morals - not necessarily because they've thought it through logically, but because their conflicting definitions make them incapable of coherent thought on the subject.

There are quite a lot of people who think there are no objective capital-m Morals, in the philosophical sense. Noticeably, they don't go around eating babies, or behaving much differently to everyone else. Presumably they have settled for small-m practical morals. So, again, something very like the distinction you are calling for is already in place.

When questions of blame and credit take center stage, people lose the capacity to think about values.

I don't see any evidence for that.

For morality to be about oughtness, so that we are able to reason about values, we need to divorce it completely from free will.

Meaning philosophical free will? Surely having a gun pointed at one's head is quite relevant to the issue of why one did not do as one ought.

ETA In summary: it is not FW versus morality. There is a link between FW and morality at the level or philosophical discourse, and another link between (another version of) FW and (another version of) morality at the pragmatic/legal level. Goetz's requirements can be satisfied by sticking at the legal/practical level. However, that is not novel. The stuff about God and the soul is largely irrelevant.