I always play Raging Barbarians and I try to make them a bit tougher by bumping up their camp healing from 10 to 20. If there are other ways to make them stronger through simple variable changes, feel free to suggest
The Authority civs don't do any better than the Progress or Tradition in my games. Everyone thinks Authority will overperform with Raging Barbarians but I don't see it. I think the reason Tradition & Progress perform better than expected is because with zero barbarians the map fills up much faster with everyone prioritizing settlers and claiming land. So you come into conflict with Authority civs much faster. With Raging Barbarians everyone has to spend the Ancient area battling barbs for survival and there's fewer Civ vs. Civ conflicts (unless the map is very crowded, but then there's no barbs anyway). By the time non-warmonger civs come into contact with the warmongers they've had more time to prepare and all their units should have 45 XP from the barbarian wars.
Since "Chill" players want easier barbarians, and "Raging" players seem to be OK with fighting through the swarms in Ancient, I would propose this:
Raging: +5 heal per turn outside of camp
Standard: no change
Chill: +10% combat bonus vs. barbs for all players
The settings I usually use are:
Tectonic Map, Large Map sometimes Standard
13 civs (or 11 on Standard)
Emperor/Epic, sometimes Emperor/Standard seed
Raging Barbarians with 20 heal per turn in camp