Several members have fabricated some type of rolling platform. One of the main issues I see, is in all probability, the TC is going to weigh between 2,000 and 5,000 pounds. That is a lot of weight to roll on casters. By hand (one person), flat ground, try pushing a car with regular tires.
When you say standard carport or garage, you need to clarify. I think most garage doors are about 7-feet tall, and I am not aware of a standard Carport height.
I am sure some of those that have accomplished what you want to do will chime in with how they did theirs.
Wayne