I shipped my Z when I moved from Michigan to Arizona last year. It was a corporate move, so they paid to ship two vehicles in an open hauler, but I had to do the Z on my own. I got a quote from the same transport company figuring that I might get a break since they were already taking two. The quote came back around $1800 for an open carrier. I then requested a quote through U Ship and got a dozen or so transport company responses. Most were around $1100, but because of my situation, none were going to work. Enclosed transport was around $1600. The best any could do was a one week pickup window and an even bigger delivery window. I was leaving on a specific date from MI, so I would have to back up the pickup at least a week before my departure. I also had rented a 30 yard dumpster to clear out anything I couldn't take to AZ and that happened to be blocking the driveway until a few days before my move. I was forced to go with the same transport company that my other cars were using. They gave me a specific date and a few hour window for pickup with about a week window for delivery.
When my cars arrived (open carrier), they were filthy, but mostly intact. The side mirror broke off along the route, but to be fair, it was weak and just broke from being shaken, not from being struck.
If you request a quote from U Ship, I highly recommend using a throw away email address. You will get dozens of emails immediately and they will keep coming for a few weeks.
We ship cars every single day at work via Reliable Carriers and I can say that paying more does not mean better care or reduced chance of damage. It all comes down to the individual driver, the position on the truck, and luck. If your car goes on the back of the truck, it could get unloaded and reloaded several times along the way. Each time they move it brings damage risk. If it's on the bottom deck, it could get dripped on from the car above, and so on.