To keep anyone interested updated: I've been working on an update for this. I'm trying out a form of scaling maintenance for cities/districts, and I've rebalanced warmongering penalties. For now I'm keeping friendship bonuses as friendship bonuses, though I still may move them to alliances later. I want to try this out with another diplomatic change, however, where there is a much more severe diplomatic penalty for declaring friendship or allying with the enemy of another empire (for an example if you're friends with Spain, and Spain has denounced or is at war with Egypt, you will have a severe diplomatic malus with Egypt--I've essentially doubled the penalty for this from -6 to -12). I've increased the warmonger penalties for declaring war so they are now closer to base game levels (but still lower), but I've halved the warmonger penalties for conquering cities. I've also halved the warmonger penalties for wiping out another Civ or city-state, and you also get a lot less warmonger penalties with Civs that have denounced or are at war with your target (80% reduction if at war--increased from 40%, and 50% reduction if denounced, increased from 20%).
I've also looked at friendship bonuses that seem a little lackluster, like Japan's or Norway's, and redoing those. I want to try and tie them into a Civ's traits if possible, but in general, I believe they should be economic boons that affect players early in the game (no later than Medieval era). I'm also trying out districts unlocking every 4 pop rather than 3 to encourage specialization and decrease district spam. The administrative precinct may also change its role in some way, possibly removing the population gating from it and/or having it reduce city maintenance.