Here's a wild thought, what if instead of garrisons being the tacked-on element to culture (and maybe science) for Authority, it was instead the core. Hear me out!
Authority starts off with a need to have a garrison to keep your populace under control. You can't master others until you master yourself. The expectation is that instead of having a single garrison per city, and that garrison tries to hunt roaming barbarians like Tradition and Progress, you need multiple units to keep the free yields rolling. Your first "building" is replaced by a unit, and if you bring a unit with a settler then the city immediately gets the yield train rolling. Different policies might add different yields to the garrison bonus, and you'd make sure that garrisons are maintenance- and supply-free.
So now you have a consistent way to keep Authority cities on-par with the free +1s, +2s and +3s of Progress/Tradition, all tied around prioritizing your army infrastructure before councils, monuments, tile improvements, etc. Add to this a new mechanic: when you DECLARE WAR, you get the garrison bonus in all of your cities for 20 turns (scaling with game speed). During this time, you can move your garrisons to battle, actually leverage your army, but you have a window before your population loses its bloodlust. It's not quite as bad as war weariness, but it hits on a different angle: the free garrison yields. Maybe the finisher lets WLTKD also count as having a garrison, to let this mechanic play out in the early game but become less important later. I even love the idea that you declare war on some random civ across the world, like you're framing them for the barbarians that you're about to clear out.
You'd still keep on-kill yields, the settling yields, all of that in the tree. But it wouldn't be what the base scaling is designed around. You have a much higher floor for the policy tree, and it's a lot easier to tune it.