But how should one choose between morality and babyeating?

Channeling my inner Eliezer, the answer is obviously that you should choose morality (since "should" is just "morality" as a verb).

Now, instead of a moral anti-realist, I'm a moral realist, a babyeating realist, and normative judgement anti-realist.

No, because normative judgement = morality.

This is almost starting to make sense, except... Suppose I say this to a babyeater: "We should sign a treaty banning the development and use of antimatter weapons." What could that possibly mean? Or if one murderer says to another "We should dump the body in the river." he is simply stating a factual falsehood?

I wonder if this is a good summary of our disagreement with Eliezer:

1. His proposed definitions of "morality" and especially "should" and "ought" are objectionable. They are just not what we mean when we use those words.
2. He classifies his metaethics as realism whereas we would classify it as anti-realism.

Out of these two, 1 is clearly both a bigger problem and where Eliezer is more obviously wrong. I really don't understand why he sticks to his position there.