Wade asked me to jump in here. I've done a fair amount of long-distance transport, pertnear all of it east of the Continental Divide. There are some really good ground transporters that just transport rescue animals, and charge amazingly little. If you could incorporate them into your transport along with Pilots N Paws you might have better luck pulling this together. Here are some that might be able to help:
Dog Runner - Runs every two weeks except Christmas week (and one other during the year). Based in Brighton, IL. Runs from Texas on one end to Maine on the other. Dave and Elaine are wonderful. $150 for a dog going from one end to the other. $30 from Spring to Plano (Houston to Dallas). They could get your dog to Kansas City if they are passing close enough to you and you can get the dog to them.
C.A.R.E. Transport - Runs from Kansas City to Denver, but I'm not sure of the schedule other than that they co-ordinate with Dog Runner to transfer dogs at Kansas City. $60. C.A.R.E. is actually a relay transport, but the folks doing it have it down to a science because they do it so much. This gets your dog to Denver, but then the mountains loom and it's winter.
P.E.T.S. LLC (Peterson Express Transport Service) - Similar to Dog Runner and covers much of the same ground. Does not connect to C.A.R.E. that I know of, but does cover more of the southeast than Dog Runner. I've not used P.E.T.S., but people who have say it's great. Cost unknown. Might come closer to you in Tennessee than Dog Runner does.
If you have trouble finding their contact information, let me know.
I also may be able to help with getting your dog from Denver down to Albuquerque. That's not a regular transport route that I know of, but there's a hound rescue group in Albuquerque that has a foster home in Denver, and they move dogs back and forth.
I'm not on the Ride Board all the time, so if you need to contact me use my e-mail address:
jdunham@texas.net.
I hope this helps.