I'm not sure that randomness from evolution and enculturation should be treated differently from random factors in the intuition-squaring process. It's randomness all the way through either way, right?

I think this statement is the fulcrum of my disagreement with your argument. You assert that "it's randomness all the way through either way". I disagree; it's not randomness all the way, not at all.

Evolution's mutations and changes are random; evolutions adaptions are not random - they happen in response to the outside world. Furthermore, the mutations and changes that survive aren't random either: they all meet the same criteria, that they didn't hamper survival.

I believe, then, that developing an internally consistent moral framework can be aided by recognizing the forces that have shaped our intuitions, and deciding whether the direction those forces are taking us is a worthy destination. We don't have to be blind and dumb slaves to Evolution any more. Not really.