So, I'm not very happy with the organizational management rules that are associated with Kingmaker and Ultimate Campaign, for unimportant reasons. So I decided to write up my own system for faction-level play (although I borrowed some ideas from Stars Without Number).
Here's the Google Drive link -
Faction Rules v2.0
Design Goals:
1) Plays fairly quickly, while allowing interesting choices from faction leaders.
2) Mechanically concrete, but flavor-light. I enjoy making up in-world descriptions for various mechanical results and events as they arise, and so do my players. So there's little hardcoded flavor.
3) Works for a variety of scales. It can do gang warfare and intergalactic warfare just as easily.
4) Accommodates weird factions that don't have a traditional state-based political structure.
5) Is chaotic and unpredictable, since it's as much of an adventure seed generator as anything else.
6) Is short, since my players are bums. (It's only 6 pages in the current draft.)
We've so far played out part of a time skip between one campaign and the next using this system, and it's had very interesting results. Maybe it'll be useful to you, and I'm happy for any suggestions!
Potential Concerns: I'm not 100% sure that the attributes are roughly on par, or that all-eggs-one-basket versus balanced-attribute playstyles are interestingly incentivized in different ways. The event charts are wildly unpredictable in their effects on the game, which may not be to your taste. Direct interactions between factions might need to be encouraged a bit more.
Potential Areas for Expansion: Rules for how PC stats and actions interact with the faction-level stuff. I pretty much just eyeball that sort of thing right now. (I might, for example, say that players can do a sidequest to recover a point of damage to an attribute instead of taking a regular faction turn to do it.) Faction-building rules might be useful, too - I just assigned stats by fiat in my campaign.
