Places like Phillips Andover, Phillips Exeter, and St. Paul’s not only have multiple courses beyond calculus but offer independent study as well. If I were you I would call up a couple of Directors of Admissions at top boarding schools and have a discussion, as well as speaking to someone at CTY. These places are used to dealing with very bright kids and may be able to give you some good advice.
What’s best for your child intellectually may not be right for her emotionally, and vice versa, so you’ll want to weight her intellectual growth with her growth in other areas. I know more than one adult who was radically advanced as a child or teen and who regrets it now, feeling that they missed out on normal peer interactions and social/emotional opportunities.