Out of curiosity, if one chooses to HS, can the kid still go to school for lab work, sports, etc?
The answer largely depends on your local school administrators and state law.
HG+ kids who are not extremely self-regulating can be VERY stressful/time-consuming to homeschool. Not because they require much help to learn-- but because it takes so much time, money, and energy to keep them on-task with something novel to learn or do.
There is simply no good out-of-the-box homeschool curriculum to use, and therefore your only real options are all "eclectic" which means huge investments of time in developing/vetting/monitoring.
Childcare is not all that difficult to manage, in our experience. The problem is in keeping the curriculum suitable and engaging on an ongoing basis.
On the other hand, I found that the experience of trying to homeschool my PGlet made me a MUCH better advocate for her with our virtual school later on. I knew very well what challenges we were up against, how flexible and NIMBLE things needed to be, and warning signs when things were becoming unbearably ill-fitting. I also knew what a Herculean thing it was to keep on top of it all.
Do think carefully about how you plan to evaluate progress and keep track of what is/isn't working. Plan in some kind of data-gathering or record-keeping method right from the start. It's always problematic to try to get credit for independent study as an HG+ homeschooler. If your studies have you working +2-4 (or more) years ahead of chronological peers... assume that you will meet with skepticism.