I used Intercity a few years ago, bringing my TR3A from Phoenix to Richmond. It was an exceptional experience. Two-level, fully enclosed trailer and very reliable personnel.
https://www.intercitylines.com/
I was unable to meet them on the Phoenix-end of the transfer, and they worked with my designee - covering every detail of the loading and shipment with him. They offered electronic status en-route and gave me an arrival time, +/- one hour. On receipt and unloading, they thoroughly inspected the vehicle with me, only leaving when I was good-to-go.
An aside, the driver invited me to climb into the trailer and check out the TR before he unloaded it. Sitting in front of it was a French Racing Blue Bugatti Type 35. I told the driver to feel free to back it out to keep the Triumph company...