Well, in my world, it means that the premises are built into saying "moral claim"; that the subject matter of "morality" is the implications of those premises, and that moral claims are true when they make true statements about these implications.

So, according to this view, moral uncertainty is just a subset of logical uncertainty, where we restrict our attention to the implication of a fixed set of moral premises. But why is it that I feel uncertain about which premises I should accept? I bet that when most people talk about moral realism and moral uncertainty, that is what they're talking about.

(and what that starting set of values would become in the limit of better knowledge and better reflection)

Why/how does/should one's moral premises change as one gains knowledge and ability to reflect? (Note that in standard decision theory one's values simply don't change this way.) It seems to me this ought to be the main topic of moral inquiry, instead of being relegated to a parenthetical remark. The subsequent working out of implications seems rather trivial by comparison.

So moral claims can be true, and it all adds up to normality in a rather mundane way... which is probably just what we ought to expect to see when we're done.

Maybe, but we're not there yet.