A few different things popped into my head as I read your post.
1. Is subject acceleration possible? Even if it doesn't cover all of her bases, it will provide challenge in one area and help make sure she learns to learn.
2. If she is socially happy, don't second guess it (unless you are afraid you wouldn't know if she was unhappy, which doesn't seem to be the case).
3. The fact a psychologist says a student needs a couple full year skips would not make the case for me. HG/PG kids all vary dramatically. My DYS son is doing pretty well for the time being (not perfect, but pretty well) with no full skips and a 2 years of math acceleration (soon to be 3). My DD, who is untested but I would guess is MG (although who knows) would probably be the one who would benefit from a full skip, she is very mature, doesn't suffer fools gladly, and highly independent.
4. I would get the math assessment tomorrow (if teacher won't get it done go to the principal), and then use that as a starting point. If she was able to go to math a couple grades up, how would you feel about the current situation? Would that address a number of your concerns.
5. If she is happy in her class without any super close friends right now, I wouldn't worry about it. I think trusting our kids about how they feel about social situations is important. I know that I sometimes project my own concerns about friendships and relationships when there really isn't an issue.
Good luck, it is great that you were able to get her to a school where she is happy. And I echo the sentiment that it is okay to take a break from advocacy - in the end, your DD will be great.
