The Vong would have to have a completely different unit structure, and technology too, most likely. Definetely city improvements would be different. It would take a lot of work, and shouldn't be done until the end. I don't think it would be impossible, just really, really hard.
For the Chiss, as someone has pointed out, it should be the Ascendancy, rather than the Chiss Empire. A good Unique Unit would be a Clawcraft, or something. Thrawn should not be a leader, as he was barely even considered Chiss after he left to join the Imperials. Maybe Baron Soontir Fel, or maybe one leader for each family; Nurodo, the other three families (don't remember their names, all I remember is that there is one for each part of government, and Nurodo is military), and the Chiss Expeditionary Defence Force. Could be too many leaders, but that's just a suggestion.
The Galactic Federation of Free Alliances should have Cal Omas, and Leia Organa Solo as leaders. Leia wasn't ever the Chief of State, but she was very influential. You could also put a couple of military leaders as other choices. The UU could be the XJ-wing, the new X-wing.
The problem with having the Imperial Remnant is that it would basically be the Empire, with Palleon instead of Vader/Thrawn or Palpatine. Maybe just add him as a third leader choice, instead of a completely different civilization. Is it possible to have a different automatic name for cities, based on the leader? If so, that would be pretty easy.
The Hutt Empire should have smugglers, or bounty hunters, as UU. It shouldn't be the Hutt Empire, but the "Unlawful" Empire, or something like that. Then you could add other crime lords, that aren't Hutts.
If you have the Old Republic as the Galactic Senate, you could rename the Ancient Old Republic too just the normal Old Republic. A little less unwieldy.
One last suggestion: Thrawn should have the Noghri. The little creatures could kill a Yuuzhan Vong with bare hands, and would do anything to help "Lady Vader" or Thrawn, or Darth Vader.