Sounds very similar to the "unschooling" movement in the 1970's. I knew of kids who attended and adults who ran various of these schools in the 1970's. By the 1990's most of these school had failed. I considered one of these schools for my son in K but decided that while it might be great for him in K-2nd I wasn't happy with it's upper grades. (It moved a few years later and is now shut down, after more than 35 years.) It didn't really have a specific gifted program, but did work with kids at their own pace.

The price does seem in line with other private schools in the area. The SF area is a very expensive place to live & that amount of tuition doesn't surprise me.