I have a drop deck you can hire. If I give you a price from Texas it will make the other fellow seem a lot more affordable.
That said I expect you will have to pay anyone for waiting time to load and unload, rig up and rig down time (installing rails to carry the car, etc.) plus road time/mileage. I doubt it will get down cheap. It cost a lot of money to do these one of a kind things when compared to a ordinary line haul, drop and hook, or other constantly repeated haul.
Good luck with your move,
~Hoss