I had good luck with www.intercitylines.com. They were not cheap, but they were VERY professional. I looked at BBB reports on companies, and some consumer opinion sites. They were the only transport company I found without at least one horror story. The worst complaint I found about them was someone who complained that shipping took a little longer than they expected.
Check with local based race teams. For example when I bought a car in California, it turned out Bobby Archer was racing at Willow Springs just north of LA, near Gorman, well, quite a bit east of Gorman, about the time I needed to take delivery. And he had space in the pro rig for one more car. That got the car from California to Fort Worth.