This thread doesn't need to turn ugly.
To the OP (Original Poster),
Let's just put it this way... whatever towing company you call should know how best to not only get your car out of the garage an onto some sort of towing vehicle, but ANY car. So call around, ask how they will get your car out, and make sure to tell them it is a Vette and ask if they will do anything differently because it is a Vette.
Ultimately, whatever company you wind up with will be responsible for making sure your car is not damaged, and if they do damage it, will be responsible to repair it.
Let us know how you make out!
Good luck.