One of the benefits of homeschooling in terms of social skills is that you have more control over the kind of peer interactions your son has. A child with developing social skills may not have the resilience to manage the "law of the jungle"-type peer interactions that tend to predominate in large, loosely-supervised settings like recess. In a homeschool setting, you can design peer social situations for success, so that he has an opportunity to practice skills he might be working on in therapy or at home, but in sheltered live situations, where he can be reinforced by experiencing meaningful success. You are also often in the vicinity, to coach him with a consistent set of cues.
One of the flags in your DS's case is that adults in the situation, and objective measures, indicate that he is successful academically, and much improved behaviorally, but he is not perceiving this about himself. Whether schooled at home or elsewhere, he needs to be in an environment with generous--but authentic--positive feedback about his successes. At the moment, he is heavily predisposed to interpret environmental feedback as negative, therefore his settings need to be quite intentional about helping him identify his strengths. Because a standard classroom is designed for bringing everyone up to an even level of development, even after the grade skip, he is probably receiving more feedback from the setting about the areas in which he lags or is nearer the median (for which the teacher may occasionally assist him), than in which he excels (for which the teacher does not need to assist him, and thus possibly gives him negligible overt attention). Remember also that any negative feedback from his previous settings likely left a mark that will need to be specifically countered; it won't just disappear because the current circumstances are relatively better. Oh, and some teachers actually praise weaker students more than stronger students (usually unconsciously), because they are trying to encourage them to do better/try harder.
We've been homeschooling ours for a few years now, but did have experiences with institutional schools. The one who finds the social impact of homeschooling to be least positive is actually the most socially skilled one, who, I think, would prefer a larger stage...
