Intuitions about morality seem to split up into two broad camps

Why are you concerning yourself with intuitions? Imagine what physics would be like if we had not abandoned intuitive concepts and turned to rational analysis. Just abolish everything done by and after Galileo Galilei, and that'd be it.

So what we should want, ideally, is a view that: (various desiderata)

There is nothing so fatal to intellectual inquiry as deciding what the answers are before the questions are asked.