Welcome!
If you have the time and means (which it sounds like might be the case), you could consider homeschooling through high school, and look for the community of peers through other kinds of affinity groups outside of institutional school--perhaps through meetups with other gifted homeschoolers. If looking in that direction, I think I would look for regions with generous and high quality dual enrollment programs, which might give your DC the option of remaining nominally in high school for a couple of extra years without running out of challenging content (sometimes especially of value to learners who play sports, dance, or participate in community theater, scouts or similar extracurriculars with their chronological peers). For example, in our area, any student age 16+, and students below that age with administrative permission, may enroll for community college or state university courses at a significantly reduced cost (occasionally free, when the state legislature bothers to fund the program), based on placement testing. Many states have similar programs.
Our experience has been that this is a much more cost-effective (not just in dollars, but in hours) approach to appropriate academic challenge without a lot of busy work, which has allowed plenty of time for "chasing down their own learning," as you say.
Of course, the appropriateness of DE depends quite a bit on the development and temperament of the specific child.
An increasing number of public high schools are also partnering with local CCs to create cohorts of dual enrollment/early college students. You could look around for those as well, but make sure to do your research, as some of them are designed for the academically advanced, and some are designed to increase access for first-gen college students (not that these are mutually exclusive by any means). The difference is that the latter sometimes use lower-level college courses (bordering on or actually remedial in nature) as an onramp to helping college enter into the world of possibilities for students who are capable of college, but otherwise might never have viewed themselves in that light. You can usually tell which is which by finding listings of how many of the supposed AA degree credits are actually transferable into the average four-year university in that state.
