Fine-tuning the polities
I have settled on the Inukari Union's government. Having Sterhon (the world) at the far end of the J2 cluster felt almost like a second capital. Of all the polities, the Union retained the most contact during the Departure (when the limit was jump-2), with 21 worlds. And so:
The Union has a parliamentary government, with a three-member presidency: one member from Core, one from Sterhon, and one from the New Stars, rotating the chairpersonship. A bureaucracy regulates interstellar commerce, and manages defense from pirates and hostile states. This leads to a certain amount of interference in planet-level politics, a constant source of controversy, but overall the Union is fairly stable.