University of Texas Southwestern Medical Center at Dallas
The above is an example of the type of program you need to get into - a local university medical school program where the professors of many specialties and subspecialties treat patients with more hard to diagnose and/or overlapping medical conditions. You can mention your dog's condition as part of your medical history. Usually your doctor needs to call for a referral but your local university program may not require it. These types of programs are good at getting together all of the resources necessary for the diagnosing and treatment of the type of symptoms you describe. I think grants and other types of helpful funding are sometimes available for help in payment if required and conditions met.
You also need to try to get your dog into a veterinary version of the same kind of thing at your local vet school, though they may have no payment help programs.