...the culture at these schools seems to be a lot about high pressure/extreme workload. To me, it seems there is a difference between work that is challenging because it is conceptually rigorous, and work that is challenging because it is so voluminous.
I have a homeschooled 9th grader. We looked at private high schools. The ones similar to the schools you've described had lots of homework. I know a number of parents whose kids go to a highly-rated prep school around here, and they told me that "You live, eat and breathe that school for four years. There is nothing else." The school has a
whole lot to offer, but my son did that cross-thing with his fingers (as in, "Begone, Evil Spirit!") when we suggested it. He was right. Who needs four or more hours of homework 7 days a week?
We had previously sent him to a very small private middle/high school that had been designed with gifted kids in mind. It was fantastic. No one questioned the idea that an eight-year-old sixth grader might be ready for algebra. I'm sorry to say that the school was acquired and moved well outside of our commuting range. However, are there any small boutique schools in your area you could look at?
DS has been homeschooling since August. So far, he's very happy and is learning a lot. He took the CTY entrance test and can take all of their courses. Some, like Forensics and their English courses, are superb and well worth the fees. He did an EPGY English class that was also excellent. This semester, in addition to CTY, we've branched out and are starting to use the University of Missouri Online High School. An advantage of "Mizzou" is that they offer tons of courses. DS is trying physics and the history of Ancient Egypt.
I have no idea if these courses will work out well. The books seem to be pretty good. They're also what I call "homemade." This means that they're designed and taught by one person who has expertise in the field. In our limited experience, DS and I have observed that his homemade courses were better than the canned ones. By "canned," I mean a course that was designed by a company and then licensed out. DS signed up for AP History via CTY and it was a canned course. It was awful, and he dropped it after two weeks. The instructor spent very little time teaching, and the format was basically a weekly email that said, "Read the chapter and take the online (multiple choice) quiz." Essays were supposed to be written in 40 minutes or less (drill for the AP exam). So, blech to that one. And it was super-expensive.
HTH.
