Like Eliezer, I see solving the question (or proving that it's a bad question) as a separate project from 'dissolving the question' by uncovering the cognitive algorithms that generate the question in the first place.

surely this empirical fact would not "dissolve" the debate with the conclusion that no form of consequentialism can be right, and therefore the whole approach should be abandoned.

No, but it shouldn't expect to arrive at correct results by engaging in human consequentialist reasoning. Perhaps we'd need to use therapy or drugs or neuroscientific tools to fix our brains so they can do consequentialist thinking without craziness, or else we'd have computers do our consequentialist thinking for us.

A deontologist could still claim, for example, that while the typical deontological rules people naively come up with to explain their intuitive emotional judgements are not very good, intuitive emotional judgements are still the only source of "morality" that we have, and some set of more sophisticated deontological rules fits those intuitions better than any other moral philosophy, including any form of consequentialism.

Yes. If deontology is to be fully killed off, one must pair a 'refutation of a mistake' with a 'dissolution to algorithm' that explains how we could have made the mistake in the first place. The present post only suggests the second part.