On reading Carrier I think that his real point is (or should be) that realism and relativism are not in conflict. Moral values, like the economic value of diamonds, may be relative but are real nonetheless. The existence of absolute moral values on the other hand is not supported by anything in his argument.
Carrier is probably correct in asserting the existence of such things as “moral facts” that are “true independent of your opinion or culture” in the sense that our moral sense probably does include principles that are the same in all human cultures, and that we may sometimes be mistaken in our judgement of what action will subsequently give us the greatest moral satisfaction. But he provides nothing to support the idea that such principles are mutually consistent or that their “value” has any meaning outside the context of human culture.
I would add that Carrier shares with Sam Harris the blunder of referring to things like “the consequences you would want most”(assuming blah blah blah) without understanding that there is probably no single real variable which measures our level of “total satisfaction” at even a single instant (let alone integrated over time).