OK, I guess I was equivocating on intuition.

But on your second paragraph: I don't think I actually disagree with you about what actually exists.

Here are some things that I'm sure you'll agree exist (or at least can exist):

• preferences and esthetics (as you mentioned)
• tacitly agreed on patterns of behaviour, or overt codes, that reduce conflict
• game theoretic strategies that encourage others to cooperate, and commitment to them either innately or by choice

Now, the term "morality", and related terms like "right" or "wrong", could be used to refer to things that don't exist, or they could be used to refer to things that do exist, like maybe some or all of the the things in that list or other things that are like them and also exist.

Now, let's consider someone who thinks, "I'm intuitively appalled by this idea, as is everyone else, but I'm going to do it anyway, because that's the morally obligatory thing to do even though most people don't think so" and analyze that in terms of things that actually exist.

Some things that actually exist that would be in favour of this point of view are:

• an aesthetic preference for a conceptually simple system combined with a willingness to bite really large bullets
• a willingness to sacrifice oneself for the greater good
• a willingness to sacrifice others for the greater good
• a perhaps unconscious tendency to show loyalty for one's tribe (EA) by sticking to tribal beliefs (Utilitarianism) in the face of reasons to the contrary

Perhaps you could construct a case for that position out of these or other reasons in a way that does not add up to "fanatic adherent of insane moral system" but that's what it's looking like to me.