I have seen a caravan setup to carry heaps of already rigged sails. It was a good idea for a rental place, even if they had to let the downhaul off a bit.
I think a lot of the masts would have ended up with a prebend in them after a while, but I am not sure that matters.
The caravan carried a lot of sails.
Have you thought about tying it to a balloon and just tethering the balloon to your car?