Thank you for the link to the article BTW! My oldest falls btwn a type 1 & type 6 on that. Advocating for her and her being accelerated is likely what pushed her more toward the type 6 part. My youngest, like your ds, was pretty close to that type 2 in elementary with some of the 3 & 4 aspects in there (b/c she's a girl and 2e).
We were advised not to push for GT placement or any accelerating by a psych despite gifted-highly gifted IQ scores. I am really, really glad that we didn't head that advice. While she is still different from a large majority of the kids in her classes, her self image is much more intact and she's learning how to work around her challenges by being better placed academically.
I'd definitely consider the Montessori strongly if you can make it work. We've generally found that having kids of similar ability to oneself (dd13 had an unusual group of HG peers in middle school) does a lot toward shrinking one's head and grounding a kid. He's a young boy. Getting him to sit still and be quiet may not be totally in the cards, but I'd bet that his social issues in class will diminish if his placement is better as well.