I'm not looking at sports as a panacea. It's just about one set of his needs to be met, ie exercise, outdoor time, sensory diet, and yes, social recognition.
Ideas:
Trampoline (even small one, indoor type)
Wii Sports (I know you said you don't watch TV--do you do game consoles?) I really think there is some value in the kinetic type games, in terms of developing eye-hand coordination, and body awareness. And sometimes siblings will even get along to play these together!
My DS learned everything there is to know about sports via video games. He also played a few team sports, the best one being baseball--I think it is less overstimulating than soccer (scared him to death) and basketball (which he is ill-suited for, physically). I know video games aren't exactly what you're looking for, but I do think for DS his encyclopedic knowledge of these helped, socially.
Playdates can be difficult when you are already over-extended. With my eldest--who craved social connections but was awkward--our strategy was to invite, invite, invite other kids over until they began to reciprocate. I had more time, then, though, with only one child.
As an aside: with my middle DS, martial arts went okay until suddenly it didn't, following a "Stranger Danger" class where they taught the kids how to get away from a predator.
He pretty much melted down and refused to ever participate again. Anxiety, obviously. Wonder if anxiety related issues are interfering with your son's enjoyment of physical stuff?
I have an idea. With a disabled child, we're eligible for three weeks family rehab every four years at lest and haven't taken any yet. I'll try to set something up in the mountains in February or so, take him out of school, not that he's missing anything, and we'll go skiing as much as we can!
Sounds like an awesome opportunity to get some respite, recreation, and family time!
Lots of positive vibes sent in your direction.
