I would defiantly try and find a different tester. You don't need to have the screen done again but don't have the full tests done with someone she isn't comfortable. Unless you live in a very remote area you can probably find someone else to do this testing.
My DS16 has been seen by a few psychologists and been fully tested by one a bit over a year ago. He is also borderline ASD but more "that gifted" and quirky. His official diagnoses talks about 'sharing some characteristics with ASD'. My son still to this day will simply NOT TALK to adults he isn't comfortable with. (It's gotten a lot better over the past year.) And if your child isn't comfortable with a tester and she doesn't comply her testing is going to come out very skewed. I also found out that many testers are really looking and trying to pin a label on your child for ASD, ADHD and have little experience with gifted kids. Most people don't bring "normal" kids in for testing and therefore assume there must be something there they can pin a label on.
Isn't it nice to have a school district that at least is trying to work with you. My DS's school was very accommodating when I gave them DS's formal report that also included anxiety disorder and wrote us up a 504 as soon as they were able. (Wish I had done it before H.S.) When I talked about his being 2E to my surprise I received understanding and not confusion.
Best of Luck I hope you find a psychologist that both of you like to test her.
