Re. high end private schools...
I think that most of the tuition goes toward infrastructure. We are close to a family who's child attends such a school. We often hear about things like:
* Overnight fieldtrips (rafting, skiing, etc.)
* School trips to foreign countries
* Parent meetings with teachers and a middle-school adviser
* Elaborate extracurricular activities, such as specialized lessons in juggling for a part in the school play
The student is clearly getting a highly personalized, top-notch education with lots of stimulation and opportunity...
But even if we could afford the tuition, this school would not work for us. Because they aren't going to let DD11 join as a 8th or 9th grader no matter how she tests (I called and asked) and I'm suspicious about their willingness and ability to support the extreme differentiation she'd need in an environment where "all of our students are gifted."
In terms of the OPs planning around tutoring, I strongly recommend combining at home learning with various classes and group activities... because it provides social stimulation and breaks up the week (the reason school kids have assemblies and other activities is to break up the monotony).
