I suspect that having a voice (or not) is a significant part of his school-based behaviors. His cognitive profile is so strong in abstract-conceptual thinking that having to follow unreasonable (or at least incompletely explained) rules and regulations all day is likely vastly frustrating. Completely aside from the lack of intellectual stimulation in his area of strength. IOW, having a better academic match would help a great deal, but it wouldn't make the collection of mundane and arbitrary rules that is most institutional schools go away.
Will the school allow you to sit in to observe his classes for a day or a few hours? You may be able to pick up on something that he has been unable to articulate.
And as to home schooling in your circumstances: one of ours is very lively, friendly, and extroverted, who loved school, hated days off, etc. (The difference is, school loved DC back, despite biting classmates in first grade!) We made the decision to home school eventually, despite DC's preferences, but with consent, and with a lengthy, bidirectional conversation about educational needs, holistic development, the zone of proximal development, and how we would make sure that the other social needs were met. It was a decision that DC understood intellectually at the time (which is why we got compliance), but wasn't happy about, but it took three years before a comment one day, out of the blue, that DC was happy, in retrospect, that we had made the parental decision to home school.
I can't tell you what's best for your child, of course, but I just wanted to throw out there that sometimes it comes down to a thoughtful, well-communicated parenting decision, which hears and takes into account the perspectives of the child, but ultimately is the loving choice of caring adults.
