Not running isn't as bad as not rolling. What city / state is the car located and what city / state is it going. Most carriers charge a dollar a mile one way. For a project like this, I would be looking for an individual that advertises in Hemmings Motor News, since the independent small guy will be better equipped to handle the move. They usually move one large car, or 2 small cars on their trailers. The bigger trucking companies have car carriers that hold 7 or 8 cars, and they need to move the cars on and off of the trailers to balance the load as they drop the cars at their destinations.
I have been using and recommending 4 Corners Auto Shippers based out of Saattle, Wa. The owners are Ellen and Jeff, their phone number is 360 210 7665. I highly recommend these people. They recently delivered my Lincoln limo, but they have moved many professional and collector cars for me.