Hi,
Welcome! I was really happy to find this place.
I really think it's possible to do both. Ie do differentiation/enrichment etc and at the same time try to do a few things to support him fitting in. The only thing I definitely would disagree with is cautioning him on speech -- it may be hard to judge which words are the ones to avoid since he's comfortable with all of them, leaving him even more self conscious about opening his mouth.
My parents, caring only about academics and classical opera, were a little oblivious to social norms in our geographic area. As such, my mom did my hair care until I was about 13. I was also dressed too child-like for some years when other kids (girls) had moved on. At the same time they unknowingly gave me wonderful gifts socially by letting me watch TV like my classmates, and buying me a few video games. Any extra piece of shared kid culture helps socially.
My DH's parents, conversely, were much more worried about social status and fitting in. DH did not fit in. I think their focus was not helpful to DH. He ended up doing pretty early experimenting with pot and alcohol which to me hearing about it at admittedly a huge distance, seems like he had absorbed their worry about fitting in (or maybe it was a genetic sort of worry). Personally I think do whatever you can silently to help a child fit in but avoid them seeing that you feel it's a big deal. So much of it isn't in their control but has to do with the dynamics of all the other kids they are around.
So anyhow... volunteer at his school or in some other way check out what the other kids wear, etc, make sure your DS does not stick out visually unless he's the one choosing to. Like are crocs "only for babies" or things like that. And then either ask DS or the teacher what TV shows and video games the kids talk about. A few hours of video games a week won't be as likely to hurt him as feeling completely left out of many school conversations.
But also see about some differentiation, even something as simple as things to do at his desk after he's finished his regular work. It doesn't have to be stamped on his head and even if it is it's probably still worth it.
Polly