I've never shipped a car, but I've read a lot of stories on the forums.
Do some reading via Google.
It seems like you get what you pay for.
Some movers are shady.
They change the price and not release the car.
Some brokers are just middlemen.
Some jerk you around with delays, trying to combine fares like a taxi.
If you want "white glove" and zero BS
it seems safer to use the big 2.
These guys were the exclusive shipper when I was at Pebble Beach
Reliable Carriers | Vehicle Transport Services
Enclosed Auto Transport, Enclosed Auto Shipping, Classic Car Storage - Horseless Carriage Carriers
http://www.intercitylines.com/
At least get a quote from these and see if the discount is worth the added risk.
Hagerty agrees
https://www.hagerty.com/articles-videos/articles/2012/11/29/Transporting-your-classic