Well that is a heck of a problem! I don't think there's a simple solution to your problem, especially considering that at this point you've concluded the problem at her school is the academic curriculum which you well know you can't do anything about. I'll try to keep my opinion short but it won't be easy. LOL
In my opinion the answer would be pretty simple if she wasn't lacking the academic challenge that she desires. Personally, academics aside, I would choose a public school. Although even saying, “Academics aside” and “school” in the same sentence is a bit of an oxymoron.
I think good public schools, keyword being good; have much better long term benefits than private schools. I've read through most of the opinions you've gotten so far and a lot of people would disagree with me. Private schools are good, they're undoubtedly for the most part, better academically and how shall we say, the caliber or quality of people and other children that they interact with at a private school is arguably better. So the private school provides better education, and probably more open doors for college opportunities. However, at a private school, depending on which one, her classmates may have a much different home life and standard of living then she does. Her classmates may vacation, in Rome and the islands, they may wear clothes and accessorize with the most expensive trendy items available, which is not necessarily bad (LOL) they will be getting dropped off and picked up in rather flashy cars, ect. The drawbacks to this, is that unless you are financially able to “keep up with the Joneses” in terms of her girlfriends and their extracurricular activities she will be the odd girl out, especially in the 9-12K classes. If you can afford to keep pace with these other families, then their is really only one major drawback I see to private school.
That major drawback is, personality diversification. That is to say, everyone that she goes to school with will most likely have substantially similar backgrounds at home and be rather like-minded. To me this is a drawback.
For example: in a public school she will interact with children from the trailer park (no offense, my cousin lives of a mobile home and love her dearly) to the very cultured an affluent. Believe it or not the cultured and affluent do send their children to public schools. In my opinion, attending school, and going through the growth of adolescents and having to “manage” all those different personalities and backgrounds will help her cope with life in general and the obstacles she may incur. In the public school she will have to deal with bullies, very ignorant children, poorly raise children, very smart children, well raised children, and so on. Also over public school friends will most likely live in the same town. Which has advantages, like her possibly being able to walk to her friend's house, the gossip of what's going on in school travels home much faster, I think the parents at a public school setting have a much better handle, on issues like drugs, bad influence children, who brought a knife or gun to school, etc. The same is also true for the school faculty and local police department. Oftentimes in public schools the faculty, attended school there as well. Probably half of the Police Department attended school together, and when they show up at school for an issue, they will take it very personally. In a public school, your daughters classmates will be the children of, local police, local small-business owners, local politicians, and of course your neighbors. In her late teens, early 20s, these can be very valuable advantages. Also, when she's older and perhaps settles down with her own family in the same town she has a very strong social network right within our community. The nature of private school just doesn't allow for these advantages. And in many cases, those types of advantages may not be that valuable throughout her life.
I'm not knocking private school in any way it has huge advantages in many areas, and she may make friends with much more influential people at a private school that a public school could ever offer. It very much depends on the school.
Private school verse public-school is a rather difficult decision and I don't think there's any right or wrong answer, it's like coming to a fork in the road and having no map or knowledge of the area, you just have to choose.
My wife and I have to make the same decision you're facing now. We happen to have a very good private school near our home, however our public school, academically and extracurricular activity wise is very good. So for us it's more of a social decision.
I just wanted to point that the foundation for her adult social skills, and people management skills, will be significantly influenced by her school environment.
Lots of great well-rounded kids graduate from both public and private schools every year. The same is true for handful of jerks.
Best wishes,
Robert