Longtime lurker for the kinja days - made an account to post a response to this question.
I used to work for a auto transport broker (actually based out of Charlotte) - https://www.sherpaautotransport.com/
They’re usually not the cheapest quote, but Sherpa focuses on delivering a more ‘high touch’ service than most. They’ll give a clear breakdown of the broker fee vs shipper fee too, and would actually reduce their broker fee to compensate a shipper before charging you any more if they didn’t quote the job perfectly. (Can’t confirm if they still do that, as I am no longer an employee.)
As others have said, you will be working with a broker in this space. Most offer a fairly similar service. IMO - it is definitely worth spending a bit more to get a better driver booked. The industry tends to be poorly organized, and it can help to have someone in your corner to help communicate things when it’s needed. Flagstaff to Charlotte is a pretty desirable route, so it shouldn’t be too hard to find someone to do the job in a timely fashion.
My one piece of advice to anyone shipping a car - take LOTS of pictures of the car before and after shipping, and do not sign the bill of lading unless it reflects exactly what you want it to say. (IE - if your car has a new scratch, don’t sign the delivery receipt without that acknowledgement). Without photo evidence and the receipt, you will have a very hard time claiming anything after the fact.
Wishing your friend the best of luck, and happy to answer any questions from the broker’s perspective for anyone on Oppo.