DeHe, with a PhD school psych and a general willingness there to work with you, I'd say do it. You're at the beginning of a long journey in any case; getting it done through school will give you a baseline of information you're going to refine later anyway.
I agree. The school psych can be a great advocate. We had luck with local school's psychologist giving our DS the WJ to complete our DYS app. Our local school is not a gifted school, and I'm pretty sure that the tester didn't have a whole lot of experience with HG kids because she was new. My thoughts were that her being a new school psychologist probably got her at least a little bit of recent training in GT kids (though maybe not). Whatever it was, she really "got" our kiddo (she had done an observation of him in pre-k and I knew she was right on), and she was willing and enthusiastic.
It sounds especially promising in your case, with a tester in a GT school who is willing to help you.
ETA - And free is an awfully nice benefit.
