Your son sounds like an ideal candidate for an independent school. He seems like a very typical seventh-grade boy.
Almost everything your kids learn about education will stick with them, and the earlier it happens the "stickier" it will be. My children's lives are very much affected by their earliest years in school.
I've worked in both K-8 and K-12 schools. Advantages of K-8 schools are that they're usually a little gentler in middle school; the MS program isn't driven (at least in part) by the Upper School, so it's more responsive to the needs of early adolescents; and the 8-to-9 transition is usually the perfect year to involve the student in that choice, since it's the year that most kids (boys, especially) become sufficiently self-aware to have meaningful input. One strong disadvantage is that your son will be in grade 8 next year, so he'd be making a transition in and out in the same year, which can be rough. Most K-8s are a little skeptical about incoming eighth graders for that reason.
The obvious advantage of a K-12 is that you don't have to make the decision and go through the process twice. If your son is definitely going to start in eighth grade, as much as I believe in K-8 schools I think this is probably your better option, though grade 8 is not an "entry year" for any independent schools, for the same reason as above. It's almost always easier to gain admission in grade 7 or 9.
That said, since he's young and behind the curve (such a nicer phrase than "immature, don't you think? LOL), have you considered your son's repeating seventh grade? Switching schools will mitigate most of the stigma attached, and the advantage of a little more confidence for a boy in middle school is hard to overstate.
For what it's worth, my wife and I both attended public schools; our kids did private schools for PK-8 and will both have attended MCPS for HS. (The older is graduating from HS this year; the younger will begin HS in the fall. The younger is a boy who repeated a grade.)
I hope that helps.
Peter
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Disclaimer: The anonymity here makes me uncomfortable; it's easy to be uninformed, personal, or simply mean-spirited if people don't identify themselves. For that reason, I have an account so you know whose words you're reading. I have more than 20 years' experience as a teacher and administrator in independent schools, and I hope I can be helpful to some folks. If you don't like something I've said, you're in good company — there's a long line of past students ahead of you.

If you want to chat further, please feel free to contact me offline: peter <at> arcpd <dot> com