After thinking about it for some time, I think I'd like to simplify my model:

In a morally relativistic society, credibility is distributed along tribal lines because there are no higher principles. Everyone is motivated to look out for oneself and the best avenue for that is a tribal alliance (as you point out "you treat nice people nicely and bad people badly", however, "nice" and "bad" devolve almost immediately into proxies for "benefits me" or "does not benefit me"). Things that would otherwise be absolutely wrong (like sexual assault or political violence) now vary morally depending on what is convenient to our tribe in the moment. Science can be swiftly rejected as racist or sexist (or whatever sin our tribe is immediately obsessed with) if it supports an inconvenient finding, but it will be back in favor next week when it produces convenient results.

In a morally absolute society, universal principles resist these selfish, tribalistic tendencies (although not completely or perfectly in all places at all times--remember we're describing a bulwark and not a panacea). We agree that sexual assault and political violence are very bad and we condemn people even in our own tribe who commit such acts. Empiricism is also venerated above personal or tribal convenience (although sophisticated empirical findings may take time to trickle down the chain of trust to the layperson).

Anyway, there are lots of holes to punch here since the topic is highly subjective and I didn't draw all of the connecting details (due to time constraints), but that's the general model.

Doesn't sound like you make a difference. Human always think in terms of benefits. It speaks about complexity of human behavior that you might not see simple facts about it. You can't reduce it to a simple formula, calculating beneficial strategy can go a long way. You may believe that it's beneficial to be a sociopath until you know what it entails.

do you believe there has ever been a morally absolute society?

I think most societies are morally absolute. Relatively few accept the "that's your truth/morality, you can't impose that on me!". This doesn't imply that all morally absolute societies have the same mores.

Nearly every society I look at has a widely diverse set of morals present in it. You might get widespread agreement that "rape is bad" but when you start to look closer there is disagreement within that about what constitutes rape (something I don't understand personally, but I can't ignore that it exists).

There is widespread disagreement about the use of force, who should care for the sick and poor and when, and so many other things.

So maybe I don't understand what you mean by a morally absolute society.

I don't understand your point of "that's your truth, you can't impose that on me." That's literally how most of us have to get along. If we were unable to accept moral differences in other people, we would be completely unable to function as a society. I don't believe there has ever been two people who have completely agreed on what's moral or not.