What could 'right' and 'wrong' mean, beyond the criteria used to make the judgment?

"Should be rewarded" and "should be punished". If there was evidence of people saying that the good should be punished, that would indicate that some people are disagreeing about the meaning of good/right. Otherwise, disagreements are about criteria for assigning the term.

So far as I can tell, only by reasoning from their pre-existing values.

But not for all of them (since some of then get discarded) and not only from moral values (since people need to value reason to be reasoned with).