You should just bribe the Hegemony inspectors, unless you want to fight them.
I can't be bothered to make new account on Starsector forums so nothing will come of these thoughts, but I think the game would benefit greatly from four additional qualities in it.
1) You should be able to define your faction politically. It could be just a dozen choices with three each, stuff like whether it is a libertarian economy, state capitalism or mercantilism etc. Same with political rights. I think human/political rights would be interesting because all the major factions in the game oligarchies at best, military dictatorships at worst. I imagine granting political rights would make fighting luddite and pirate infiltrators harder, but increase immigration. All of these choices would naturally have an effect on faction relations.
2) I think there should be some special solar systems to be found, especially once the large sector size gets added in. Stuff like an isolationist fringe colony out on the rim, automated refueling station orbiting a gas giant, little things like that to add atmosphere. Plus I kind of think decivilized planets should be special to colonize, requiring military presence (marines) in addition to crew, but having higher initial population growth (portraying wild natives rejoining civilization).
3) I think the game would benefit from Stellaris-like end game threats. So one game the Remnants active and start attacking everyone again, in another game the Hegemony starts an interstellar war, in another Luddites get taken over by the Path who start a Jihad/Crusade, striking against all the terraforming infrastructure etc, in another one of the gates activates for a moment to spit out a Domain fleet that was stuck in limbo between the worlds. Things that could completely change the world and challenge the player.
4) I think you should be able to retire, in the same sense as in Prospector, after which the game would tell a short story about what happened to you. Maybe you could choose how you retire; becoming an interstellar emperor is very different from outfitting a million credit expedition and leaving to find out what happened to Earth.