Why? How does being able to be farther from, or closer to, reflective equilibrium, assert something about the existence of better values?

That's not my assertion; it's yours. "Consider an even more significant moral advance", you wrote in your section about masculinity. Are you being facetious, or do you believe that was a moral advance? If it was, how do we know?

Could you explain what you mean by "reflective equilibrium", if it's not the standard definition?

My argument about equilibrium is simply that moral changes over time are not biased to bring a moral system closer to equilibrium. It is a separate argument from whether or not those changes are moral improvements.

It seems to me that these two arguments are also different:

Moral changes over time do not tend to bring a moral system closer to equilibrium.

and Moral changes over time ought not bring a moral system closer to equilibrium.

It seems to me that you are making a case for 1, but using it as an argument for 2. Am I still missing something?