My neighbor says don't raise the floor in the room created from the original garage - that he's always seen moisture problems when people do that. I'm thinking that when extending the heat and air out there of putting a couple of small ducts under the floor at the far end and a couple of open vents at the near end (back toward the return) as a way of moving air through what becomes a crawl space. It's a sealed and insulated area so any heat or cooling ducted under there isn't really lost to the outside. It moves the air and keeps the environment in the space under the living area close to what you want in the living area - also minimizes heat loss through the floor. It looks like one of the design concepts these days is controlled crawl spaces to do something similar.
The ceiling in that room is the same as the rest of the house, so the biggest other obstacle may be raising the outside door, but that seems doable. The new garage has a lower ceiling, so the only idea I have is a cutout in the room with steps down to the current garage door. Just have to put railings around like you see in a lot of open upper floors with stairs descending to the lower floor. Looses some useable space, but it's a huge room - it was at least a very spacious two car garage.
Those are at least a couple ideas to discuss with the contractor. If you've got any thoughts on them, they are always welcome.