First, if everyone acts as if agreement is possible, that tends to make it much more likely that agreement is, in fact, possible. The second step is a meta-ethical analysis which says that, if everyone freely and rationally agrees on a set of norms, virtues, etc., that is morality.

I agree. But I think that people act as if agreement is possible not because they are thinking of morality in the consensus sense but rather that they are thinking of morality as an actual law external to people. For many of them, perhaps, even the law of God.

I wonder if there's any experimental philosophy on lay people's thoughts on meta-ethics. It would be interesting to see, for sure.

If there are behavior codes you live by but you don't think you could convince others to live by, you could call that "morality" if you insist. In that case, the rules that we all can rationally agree to cooperate under aren't all of morality, but just a part of it - "justice", maybe.

You're right that perhaps we're debating definitions and not substance. But I think you'd be hardpressed to come up with what behaviors are actually in the "consensus morality". And it's going to end up a lot like cultural relativism.

What I'd advocate is more of an ends relativism -- actually making things clearer by specifically stating which normative/moral ends we're dealing with. For example, we could contrast the claim "One ought to be a vegetarian (relative to the end of utilitarianism)" versus the claim "One is ethically permitted to eat meat (relative to the common moral beliefs of our culture)".