I agree with much of your analysis - particularly the analogy to geometry, where, as you point out, the heuristic works. That heuristic is also useful in science. And in other branches of philosophy besides ethics.

The puzzle this post presents is: why do we have a tendency to accept moral philosophies that do not fit all of our existing values? Why do we find it natural or attractive to simplify our moral intuitions?

Here’s my idea: we have a heuristic that in effect says, if many related beliefs or intuitions all fit a certain pattern or logical structure, but a few don’t, the ones that don’t fit are probably caused by cognitive errors and should be dropped and regenerated from the underlying pattern or structure.

Given that the heuristic is so useful in other areas, I have to ask, "How you can be sure it is wrong to use it in ethics?"

Also, I think that the intuitions that don't fit into the logical structure or system are not usually discarded or replaced. Instead, I think they are often simply reclassified - if they can no longer be justified as intrinsic values, a just-so story is constructed to explain them as instrumental values, or perhaps as evo-psych artifacts of an ancestral environment which no longer applies.