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Contact your local dealer for recommendations.... they are coordinating the movement of cars all the time. Any car dealer. Price can be determined by loads in and out bound and or where the driver is domiciled ... you can optimize that if you are flexible. If you are interested in that "white glove" service, you are going to pay no matter what.
I hired "Door to door" transport to get my Porsche from Texas to Portland Oregon. The whole process went very smoothly with no complications, no damage to my car and the drivers were fine fellows. The carrier was open and my car arrived with a little coating of dust but no other damage. This was through Ebay and Door to door made the lowest bid.
Intercity Lines is the best of breed, and Reliable is about as good. I just bought another car from CA and I'm having Intercity ship. Less than $2K enclosed. They wrap the whole car in plastic. I used them when I bought my last 928 from CA to Pitt, so this will be my second time using them. They are Rennlist sponsors, and give a small discount to members (and PCA members too). They own their own trucks, and their drivers are their employees - no contract or broker situations. Wayne Carini of Chasing Classic Cars uses them all the time.