If Exotic does not work out for you, try Thomas Sunday, Inc. Tom's operation is located in PA, but his trucks travel the entire country. I used Tom because he is a Corvette guy, a member of the Cumberland Valley Corvette Club ( and NCCC club in the East Region) and I had gotten a good recommendation on him. When I moved to Florida permanently in 2007, this company did a great job for me. They transported two of my three Vettes ('69 & the '04 Z16) from Maryland to Ft Myers. They picked my cars up on time, they never moved from the truck that picked them up until they arrived in Ft Myers and I took delivery without a scratch on either one. They also arrived when they told me they would arrive.
They were not the cheapest quote that I got for the two Vettes, but they also were not the highest price. If I had to move my cars again, I would call Thomas Sunday because of the job he did for me the first time.
Here is a link to his site.
http://www.sundayautotransport.com/
I hope this helps. Good luck shipping your Vette to Texas!
Rich