Is this a car you care about for a very specific reason? (Collectable, sentimental, etc?).
While it may cost more than general movers, consider the type of business mentioned above that specializes, you may have better luck.
Several years ago, when a large number of my coworkers re-located approximately 2/3 of the way across the country, the large general moving company that our employer arranged for that covered auto transportation was problematic for some folks. Damage to vehicles, in one case trying to replace a windshield without even telling the owner they replaced it (they noticed one of their stickers was missing, guess the movers hoped they wouldn't!)! The point is a mass "get r done" mover that is just doing bulk moves may be more careless than some smaller business that might cost a few bucks more. Just another item to consider, particularly if you really like the car.
-Dave
