Ok maybe I could change the Vulcan to something else (I just love Vulcans and thought seeing one as a Counsellor would be an interesting new perspective on them). Since ENT got a good new look for the Andorians I've wanted to see more of them and dealing with the slow demise of their species could be explored further.
As for the Trill CO, if Trek were to ever have an alien Captain I think it would have to be from a race that looks more or less human or else risk alienating (no pun intended) new/casual viewers. But that's just my thought on the matter.
If you'd like, I could go with Captain Laurn Rhata from Nigala IV, a three-eyed, mottled green/blue skinned, long eared CO instead, who has to spend at least several hours a day immersed in the native waters of her homeworld.
Depending on how you break down the crew, there is the potential to add lots of new alien races. For example if the main cast was: CO, XO, Conn, Ops, Chief Engineer, Security Chief, Tactical Officer, Counsellor, CMO, Science Officer. That's ten characters to play with, say four of which are human (random selection of: XO, Engineer, Tactical, CMO), that still leaves six alien characters to cast. Even if three were from previously established species there are still three more to be very creative with.
Whatever happened, there would be a lot of aliens in the background, to show the ship as being a diverse population and not just all human (or human-looking species).