^ I too have a son (S23) who is >> 99.9th percentile; like the OP’s S23, he also has some executive functioning issues, and has been diagnosed with a Central Auditory Processing disorder, for which he wears a customized filter and has some recommendations for school accomodations. He goes to a GT magnet and is followed by a “support team”. He is strong academically overall but quite “pointy” in several areas and off the charts in a couple (especially in terms of artistic ability and engineering/fabrication/design), so his situation seems a bit different from the OP’s case; my experience is that dealing with any of these > 99.9th percentile kids requires extremely individual attention and adjustments.
In my son’s case, we’ve found regular schooling to be a challenge but to be beneficial in terms of developing socialization skills and learning to function in a broader environment (“raising the whole kid”, to use @calmom’s term). My son has met the qualifying criteria for programs like SET and Davidson, but we haven’t applied - I was quite interested in them when he was younger, but as he matures I see less and less benefit. I do a lot of supplemental “homeschooling”, acceleration/enrichment, and support for advanced ECs, all on top of his regular schooling.
For math, I would agree that AoPS is a great resource, and would also strongly suggest looking at the IMACS math and computer science online courses, which provide enrichment as well as acceleration. The EMF course in particular builds a rigorous foundation which introduces abstract algebra by middle school level. My son had done AoPS algebra I in 5th grade, but found the eIMACS EMF courses challenging and fun. He is also doing their Univeristy-level computer science courses. They have a very different approach from AoPS, which is very focused on problem solving and competition math.
I agree with @sbjdorlo that finding the right school and advocating is critical, and is an ongoing challenge. Homeschooling may work well for some, but not for others. Every situation is so different, both in terms of the child and in terms of the resources and options availalble. Acceleration works well in many cases but can leave gaps. Programs like Stanford OHS can work well, but are fairly structured and could be challenging for someone with EF issues, even if they are intellectually suitable. Early college programs work well in some cases, but often social development lags behind intellectual development. Pushing a highly pointy kid who is highly accelerated in mainly math and who also has EF issues too quickly could be tricky, to say the least.
Testing can be very useful to document abilities and identify confounding factors (it was testing which led to my son’s Auditory Processing Disorder being developed). The Gifted Development Center in Westminster, Colorado has the largest data base of highly gifted children in the world, and 30 years experience identifying and advocating for such individuals; testing is expensive, but can be well worth it (and is also important if you do want to apply to Davidson Young Scholars, as they require documented testing).
@Twoin18 , good luck, and feel free to PM.