Jason, Best of luck on your move.......Safe travels!
DFW is an odd area for the big transporters.......I recall horseless carriage, intercity and reliable did not utilize routes there....I found that out when I moved from there to Ohio......The only one left was Passport and I was thoroughly pleased...
My first choice was reliable and second was HC......Check with them to see if they can from where you're at...
I would suggest based on the quality of your car to have them strap the wheels....Be sure to have a California car cover any other cover the big guys will not allow on the car during transport.....They should also lay a thin sheet of plastic over top of your car and tie to the sides inside the hauler......Specify not to juggle your car around either.....Furthermore, I tipped the driver very well, which they NEVER get and the appreciation was shown with the care of my car......