hiker, it has been rather quiet around here, of late...
But first, yes, many parents here have had the same challenges with finding a good fit for each tier of schooling. And one of the main messages I think should be conveyed is that you know best how your family decisions fit your family's needs, so when other parents (or strangers) give you unsolicited (positive or negative) feedback on whatever you end up choosing to do, don't feel obligated to do more than listen politely and turn the conversation.
And now for our personal experience and (one hopes, requested!) thoughts:
We've used public, private, homeschool coop and independent homeschooling with our children. And I've worked in public schools, including those with congregated/sub-sep gifted programs, AP and dual enrollment. While none of our children have been formally identified as GT, evaluation of this kind is my profession, and I think I have a pretty good idea of each one's shape.
Your DC's stage is around the point at which we pulled our DC1 out of a delightful tiny private school to join the other sibs in homeschooling, not because we were dissatisfied with the school, but simply because they had run out of content, since the school ended at grade 8. Up until then, they had been quite flexible and collaborative about making instructional and placement adjustments for our child, including hiring a college adjunct (conveniently, already a member of the school community) to teach a pair of algebra I students. At that point, we did a combination of independent homeschooling for core content areas and homeschool coop for electives, labs and enrichment. We were in a position to have one parent home full time (working from home, strictly speaking) and one parent working full time (and I do recognize that school year full time has far more flexibility than full time in other professions), so childcare was not the consideration it might be for some other families. The coop we joined was not specifically focused on GT learners, but we also weren't relying on it for any substantive academic work. That particular coop was not a dropoff (every family had to have an adult representative present at all times), but there are others in our area that do have dropoff classes.
You might investigate existing coops in your area, with an eye, for example, to some of the needs you've listed, such as some level of childcare for a specific number of hours per week, compatible community/peers, engaging enrichment, instruction or extracurriculars that match your child's interests and your family's values. If the peers your DC already knows don't appear to be likely options for a coop, then perhaps an existing coop might have options for peers.
In our case, we stayed with the coop for a few years, until the year DC1 began taking a full time university load as a dual enrollment student and DC2 went to public high school, and so it became less valuable to our family to maintain a connection with the group.
Another factor is that homeschooling is not restricted to the hours of 8-2. If you have any flexibility in your work hours/remote work, it might also be possible to do some of the core academics through focused nights or afternoons at tutoring centers, such as Russian School of Math or Kumon. If the sessions are long enough for you to accomplish anything in your own work, that might be one way to get some of your own hours in while giving your DC access to quality instruction. Along the same lines, schooling and childcare do not need to be as conflated as our b&m system has. It does not take 30 hours a week to effectively challenge and school a GT homeschooler. If you can decouple childcare from schooling, you may be able to find childcare solutions that are simply safe, caring environments for DC to do independent creative, learning and social explorations, and then wait to do school after your work hours.
Consider, many homeschoolers find 2 hrs/day to be perfectly adequate. The conventional school year is 180 days/year. That comes to 360 hours/year. Spread out over the year, that's less than an hour a day of focused instruction. (Obviously, you don't have to feel obligated to cover every subject every day, either.) And if you're actually doing year-round schooling, you'll probably be able to speed through the first 10-20% of each year's new curriculum, which is almost all review/reteaching of the previous year's summer learning loss. (Actually, even if you're not year-round, you might be able to skim through this with a bright child.)
Academically, homeschooling was by far the most freeing for our children. If there hadn't been other important reasons for public high school, the first couple of years there would have been rather a waste of time for DC2, as even in the advanced/honors track, DC had to tolerate two years of repetition in math at the beginning. (The pandemic, in a bit of a twist, allowed for some recoupment during the latter two years, when many more college courses became accessible for real-time remote dual enrollment.)
