I have used Reliable Carriers before .......
http://www.reliablecarriers.com/
sometimes there is a wait for them to get full loads going each way so that they fill their trailer . They hauled new Vipers for Chrysler as well as Concept Show cars for GM, Ford, Chrysle and others - owner is a car nut too I heard.
A neighbor uses them also to ship 2 cars between Detroit and Florida each year as the seasons change . He has never had an issue with them.
If you get Hemmings Motor News you will find MANY similar companies as well - the big name ones will jump out at ya . Good luck , Bill