I bought a T-bird in San Jose a few years back, used D.A.S. (e-bay’s shipper) with the "enclosed option" selected for shipment to NJ. Car was pretty dirty when I got it (something like 2 weeks in transit). They did a good job, but that is a "$ low end" car. I suspect that it sat outside at the terminals where it changed trucks(?). The price was very good.
The Shelby guys also like Intercity Auto transport,Reliable Auto transport, and Horseless Carriage auto transport – they are mostly dealing with "better" cars.
Good luck.