In terms of moral theory, we appear to have made no progress at all. We don't even agree on definitions.
But defining terms is the trivial part of any theory; if you concede that we haven't even gotten that far (and that term-defining is trivial), then you'll have a much harder time arguing that if we did agree on definitions we'd still have made no progress. You can't argue that, because if we all have differing term definitions, then that on its own predicts radical disagreement about almost anything; there is no need to posit a further explanation.
If morality paid rent in anticipated experience
Morality pays rent in anticipated experience in the same three basic ways that mathematics does:
Knowing about morality helps us predict the behavior of moralists, just as knowing about mathematics helps us predict the behavior of mathematicians (including their creations). If you know that people think murder is bad, you can help predict why murder is so rare; just as knowing mathematicians' beliefs about natural numbers helps us predict what funny squiggly lines will occur on calculators. This, of course, doesn't require any commitment to moral realism, just as it doesn't require a commitment to mathematical realism.
Inasmuch as the structure of moral reasoning mirrors the structure of physical systems, we can predict how physical systems will change based on what our moral axioms output. For instance, if our moral axioms are carefully tuned to parallel the distribution of suffering in the world, we can use them to predict what sorts of brain-states will be physically instantiated if we perform certain behaviors. Similarly, if our number axioms are carefully tuned to parallel the changes in physical objects (and heaps thereof) in the world, we can use them to predict how physical objects will change when we translate them in spacetime.
Inasmuch as our intuitions give rise to our convictions about mathematics and morality, we can use the aforementioned convictions to predict our own future intuitions. In particular, an especially regimented mathematics or morality, that arises from highly intuitive axioms we accept, will often allow us to algorithmically generate what we would reflectively find most intuitive before we can even process the information sufficiently to generate the intuition. A calculator gives us the most intuitive and reflectively stable value for 142857 times 7 before we've gone to the trouble of understanding why or that this is the most intuitive value; similarly, a sufficiently advanced utility-calculator, programmed with the rules you find most reflectively intuitive, would generate the ultimately intuitive answers for moral dilemmas before you'd even gone to the trouble of figuring out on your own what you find most intuitive. And your future intuitions are future experiences; so the propositions of mathematics and morality, interestingly enough, serve as predictors for your own future mental states, at least when those mental states are sufficiently careful and thought out.
But all of these are to some extent indirect. It's not as though we directly observe that SSSSSSS0 is prime, any more than we directly observe that murder is bad. We either take it as a given, or derive it from something else we take as a given; but regardless, there can be plenty of indirect ways that the 'logical' discourse in question helps us better navigate, manipulate, and predict our environments.
If morality paid rent in anticipated experience, I'd expect societies that had more correct morality to do better and societies with less correct morality to do worse.
There's a problem here: What are we using to evaluate 'doing better' vs. 'doing worse'? We often use moral superiority itself as an important measure of 'betterness;' we think it's morally right or optimal to maximize human well-being, so we judge societies that do a good job of this as 'better.' At the very least, moral considerations like this seem to be a part of what we mean by 'better.' If you're trying to bracket that kind of success, then it's not clear to me what you even mean by 'better' or 'prosperity' here. Are you asking whether moral fortitude correlates with GDP?
(Some common senses of "moral fortitude" definitely cause GDP, at minimum in the form of trust between businesspeople and less predatory bureaucrats. But this part is equally true of Babyeaters.)
What do I mean by "morality isn't logical"? I mean in the same sense that mathematics is logical but literary criticism isn't: the "reasoning" we use to think about morality doesn't resemble logical reasoning. All systems of logic, that I'm aware of, have a concept of proof and a method of verifying with high degree of certainty whether an argument constitutes a proof. As long as the logic is consistent (and we have good reason to think that many of them are), once we verify a proof we can accept its conclusion without worrying that there may be another proof that makes the opposite conclusion. With morality though, we have no such method, and people all the time make moral arguments that can be reversed or called into question by other moral arguments. (Edit: For an example of this, see these posts.)
Without being a system of logic, moral philosophical reasoning likely (or at least plausibly) doesn't have any of the nice properties that a well-constructed system of logic would have, for example, consistency, validity, soundness, or even the more basic property that considering arguments in a different order, or in a different mood, won't cause a person to accept an entirely different set of conclusions. For all we know, somebody trying to reason about a moral concept like "fairness" may just be taking a random walk as they move from one conclusion to another based on moral arguments they encounter or think up.
In a recent post, Eliezer said "morality is logic", by which he seems to mean... well, I'm still not exactly sure what, but one interpretation is that a person's cognition about morality can be described as an algorithm, and that algorithm can be studied using logical reasoning. (Which of course is true, but in that sense both math and literary criticism as well as every other subject of human study would be logic.) In any case, I don't think Eliezer is explicitly claiming that an algorithm-for-thinking-about-morality constitutes an algorithm-for-doing-logic, but I worry that the characterization of "morality is logic" may cause some connotations of "logic" to be inappropriately sneaked into "morality". For example Eliezer seems to (at least at one point) assume that considering moral arguments in a different order won't cause a human to accept an entirely different set of conclusions, and maybe this is why. To fight this potential sneaking of connotations, I suggest that when you see the phrase "morality is logic", remind yourself that morality isn't logical.