Does your car move under its own power? ie. can it be driven onto a transporter? If it has to be pulled onto a trailer or transporter it usually falls into another category more like towing, which is more expensive.
I used a transport company from Toyota of Seattle to Sacramento (Roseville, actually) to have my battery replaced in 2019, and I used a transport company I linked to in that post. I didn't babysit it, but the car arrived undamaged so . . . [shrug]?
At the time, it was much cheaper (by around $400) to ship south, than the return trip north, FWIW.