Asperger Syndrome Support Group
Asperger syndrome - also referred to as Asperger's syndrome, Asperger's, Aspergers or just AS - is one of five neurobiological pervasive developmental disorders (PDD), and is characterized by deficiencies in social and communication skills, normal to above normal intelligence, and standard language development.
Alternatively, since you're not constrained by insurance, you may be able to negotiate with someone prominent in AS therapies in Austin or TX or even like Tony Atwood to see if he knows anybody willing to do this. You may have to travel but that might be an open door. Again, "Who do you know?" Eg: "Who do you know who might be willing to do testing for a reduced fee? Here's my situation-". Important not to say "Do you know anyone who..." which could easily end in "no". The former asks the listener to think and consider which is what you want.
Do you feel comfortable talking with someone from the school where you teach or the teacher's union about getting an exception with your insurance? Not allowing for testing is antiquated, but adults don't get thought of with AS.
With all of these ideas, it may be smart to get a letter from your doc or other professional who knows you, indicating the need for the testing. May well not be necessary but it would carry weight with those whose help you need. Good luck!