Another thing to try, ask some of the classic and even regular dealers in your area who they deal with on a regular basis. I'm sure they can provide you names of companies that they have done business with.
Trick is call a number of companies and your best price will come with a transport company that have other cars going to the state you are aiming for.
Last car cost from GA to CA $750 but had to wait 30 day for them to pick up and my car was number six when they arrived.
If I was in a hurry it would have been $1800 with one company and $2000 about with another.
I went this route once. They ask for a nonrefundable deposit. They set up a pickup date. Say the driver will call you. 2 weeks after the scheduled pickup no call. If they can't find a driver to do the job for the quoted price you are out the deposit. Call shippers directly.
Thats the thing with uship though, sometimes you are dealing with the actual driver, other times you are dealing with reps from companies trying to break the backs of their drivers. Reps from companies treat it like they are making a special trip for you.
Speaking of Uship, I remember watching the boobs (literal and figuratively) on that show "Shipping Wars". No way would I want some of those people moving a car across the country for me. Only one that was competent was the pony tailed guy named Roy. I'm sure it's better in real life but that show was a anti-advertisement for UShip.
i'll hook up my trailer and go fetch my own . finished $$ car pay up for top shelf haulers. if it does not run most quality shippers will pass . i missed a good buy on a 49 olds years ago . solid car but half dissembled and not running. nobody would haul it .