I would have given that shipper zero stars and written a scathing review of them. They are the experts on shipping, should warn customers of difficulties encountered in shipping, and provide solutions to the customers. Those solutions might cost extra, like car covers of some sort, but the onus is on them. Customers are not considered experts, the vendor of a service or product is. That is why we hear of crazy settlements in ladder cases. The ladder manufacturer did not warn customers of common hazards and paid the price. It seems to me the shippers that provide unsatisfactory serves of the Tempe you describe need to lose some law suits to make the cars as good as before the shipment. If they lose enough money, maybe they will start acting responsibly.
You canât prevent every possible damage scenario. Maybe you could find a place that will handle it differently and not do any swapping but Iâd think that would be difficult to find and expensive if they do. Canât hurt to ask. I wouldnât hesitate to pay extra for the covered option just to avoid those potential avenues for damage. Then- take pictures! lots of them. Note the odometer mileage when they take possession.
Donât be rushed when they deliver it and ask you to sign their form. The drivers want to take off and may try to pressure you to sign so they can take off. Take your time to inspect the car. Be sure to speak up about anything and make them note it on the inspection form. Check the delivered odometer and make note of it on the form as well if it is out of the ordinary like 1-2 miles max.
My experience agrees about not being able to choose where the car goes on the carrier. Sorry if it seemed I was suggesting otherwise.
The possible switch in carriers probably depends on many factors, including start/end locations, the shipping agent or carrier used, etc. My car was apparently with the same guy and rig from VA to CA.
Itâs always a big negative when property damage happens under other peopleâs watch and often a pain to deal with insurance. Did your own insurance on the car not help you at all?
Of course, you could pay someone to simply drive it.
I remember the first Cannonball Baker Cross country run, probably many years ago, two young men contracted to drive a nice Cadillac to California from NYC. 
They were instructed to drive well below the speed limit and to stop at dark for the night. As long as they kept it down around 105 the cops left them alone. And, since it was Cannonball Baker Run, they drove through with minimum stops for restroom and gas or sleeping.
They noted it used no oil in a nearly 4000 mile high speed drive, and I would not have expected it to. But, I wonder about the suspension hitting road defects at 105 mph?
Anyway, what the owner didnât know, didnât get them killed.
I certainly am not saying all hired drivers are going to enter your baby in the Cannonball Baker Run.
I wonder if anyone else remembers that incident?
I loved this movie when it came out, might not now, âVanishing Pointâ
âKowalski works for a car delivery service. He takes delivery of a 1970 Dodge Challenger to take from Colorado to San Francisco, California. Shortly after pickup, he takes a bet to get the car there in less than 15 hours. After a few run-ins with motorcycle cops and highway patrol they start a chase to bring him into custody. Along the way, Kowalski is guided by Supersoul - a blind DJ with a police radio scanner. Throw in lots of chase scenes, gay hitchhikers, a naked woman riding a motorbike, lots of Mopar and youâve got a great cult hit from the early 70âs.â
In my neck of the woods, this is the company that local collectors of Studebakers and Packards use to transport their vehicles to Florida for the winter, and then back to the rolling hills of Somerset County, NJ, for the summer:
http://www.horselesscarriage.com/
Their reputation isâŠsterling.
thanks
Andrea
The OP does not say where they are moving to but if it is a place like California that has emission inspections I wonder if it would be better to just sell it and purchase something after they get there. Of course the vehicle might pass but it might be worth while to know before making a decision.
Yes, see them on I95
Iâve never done it, but Iâd bet that if you attended a custom car show of any significance and asked around youâd be able to get some good references. Youâd also have a good day. Even if you didnât get any good references.
I havenât had a car towed on a hook for at least 30 years. RWD, FWD, or AWD were all flatbedded.
I would consider âVanishing Pointâ a PSA (Public Service Announcement) for not using a âprofessional driverâ!
I suppose, but it was a great movie at the time, I am going to see if I can pull it up on netflix, probably a disappointment in the making 
I watched VP for the third time about 2 years ago. I still enjoyed it. PSA comment was a joke.