As for the GC, not the exorcist. That would break the no inherent carriers. If that was the choice, why not just include the Dominion since it is in the original fluff anyways.
I would say Avenger, Vengeance or Executor. Vengeance is the best balanced of the choices, with the mix of weapons. I feel the Avenger and Executor are better fits though. Honestly, I think the Avenger is the best fit, but you could put both the Vengeance and Avenger in. Makes up for the lower than average ship selection options and 4:1 reserves rule without breaking the list. I would shy away from the Executor. While it would be nice and can make sense from a fluff perspective, it could be abused as a Native of the BFB list, and be taken as reserves in other IN fleets, without having to be subject to "Strange Happenings"