I just had a 2004 shipped from Rochester, Minnesota to Manassas, Virginia. The carrier was Run-N-Hard Auto Transport out of Ohio. The car was carried on one of those big trailers with 8 other cars (including an antique Bugatti) and arrived in good shape. (The car had one small mark on the clear bra from the hook, I believe.) The driver was experienced; he had worked 25 years for General Motors. I believe his name was Tim, and I would trust my car with him.
The company requires cash payment (it cost me $500) due on delivery, and the driver won't deliver to a residential neighborhood because the truck is so big. I had to drive a mile or so pick up the car.
If you decide to use them and can't find their number on the Internet, let me know and I will sift through my emails to find it.
Good luck, and after my experience, I would recommend shipping. It saves a lot of hassle, including leaving your car outside a motel or in a hotel garage while driving home.