OK so I have been thinking more critically of my experience with math, and I may just have to agree with the others. Even though I am far from a math whiz like many of the kids here, 6th and 7th grade math was a complete waste, I know that I could have taken algebra in 6th instead of 8th and not been wanting to bang my head on the desk or hide a book behind the math text.
The smart girls dumbing down thing (I think also mixed with some imposter syndrome for fun) came up in high school--I chose not to take the most challenging classes (although my excellent, public highly-competitive hs was very accomodating to those who wanted acceleration--i.e. my brother did one year of math over the summer and was able to take 2 years of AP calc., and there were a handful of kids each year who progressed much further than he did and were well supported by the school)
But, my parents, teachers, and guidance counselors didn't ask why or encourage me to take the higher level--despite straight As in math and 99% on standardized tests. So I would say that even in a highly regarded ps, parents still need to be more involved than mine were. (Also I guess typical of a gifted girl who appears to have it all together, is compliant, and doesn't cause problems and they trusted that I knew what I was doing...which I didn't)
So all that to say...my ideal school would be a public single-sex gifted school. But since I have not encountered one, I guess I might go for the public in your situation. Despite the fact that, again, the bright/gifted boys in my classes were the ones snickering in the back when I answered questions and appeared excited about learning (and this continued in hs even in AP classes), and despite the fact that the limited bullying and mean-girl stuff that happened in 7th grade was about boys, and despite the fact that I was actually subjected to what in the work-place would be called sexual harassment by some boys. Again not all--one of my best friends from toddlerhood through hs graduation was a (gifted) boy. And many of my close friends in college were kind boys.
I would read Rosalind Wiseman's books and I also really love the book Hold on to your kids--I think both would be appropriate as your dd enters middle school.
Re: girls schools--my husband's boss went to girls schools in New England and then Cornell, and she is highly successful and has reached a level that very few women in his industry reach. She seems to have been perfectly well prepared to work with men. (And I am currently in a rather intense conversation with her about her dd8 who is certainly gifted and mom is in gifted denial).
Good luck with your decision--please keep us updated.