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What's so great about reflective equilibrium  -- either the kind Rawls wants or the kind Held wants?

As near as I can understand it, Rawls is putting forward what some philosophers call a "coherence argument" for his moral principles. At least, that's how I understand his use of reflective equilibrium. He wants to avoid difficult issues related to "foundationalism" as Vera calls it. But does he succeed?

Let's assume that his principles fit with our considered judgments. They "save the data" as philosophers of science sometimes say. But what good is that? They have no foundation outside our opinions and attitudes. Isn't there something more?

Some philosophers have asked, what is the "justificatory force" of a coherence argument in morals? Here's what David Lyons writes:

Much more important, the justificatory force of coherence arguments is unclear....We seem to be 'testing' principles by comparing them with given 'data.' Because the latter (our shared, considered moral judgments) are impartial, confidently made, and so on, we can, indeed, regard them as reliably reflecting our basic moral convictions. But we can still wonder whether they express any more than arbitrary committments or sentiments that we happen now to share. To regard such an argument as justifying moral principles thus seems to assume either a complacent moral conventionalism or else a mysterious 'intuitionism' about basic moral 'data.' [See Daniels, p. 146.]

What do we do when someone challenges our considered judgments? What do we do when someone develops a consistent moral system that is built around different considered judgments? Perhaps the Ku Klux Klan or the German National Socialists could do this as well as anyone. Do we take a vote?

Another way to put it is to ask whether right and wrong are something other than the product of an agreement between people. Perhaps they have other foundations? Or if they don't, maybe we are up a creek without a paddle!