I think much of Linda Silverman's work is not really research at all as understood in the scientific community. She typically studies the children who come to her at the GDC. She has such a high profile that those children are unlikely to be representative of any population, even if there were no other problems with her work. Clearly she has a great deal of expertise with gifted children and her opinions are worth listening to, but also, she's heavily invested in the learning styles stuff so it's unsurprising she's slow to drop it in the face of evidence that it's not useful. I'd suggest considering her writings as possible sources of good ideas, but not letting them override your own knowledge of your DS.
Here's a lay summary and link to one debunking article.
I didn't say DYS kids must have social issues! Of course not all do. But DYS exists to help solve
problems that profoundly gifted children have, and one common problem is difficulty in relating to age peers because their interests and ways of interacting are very different.
Honestly I think you should relax, pick the school you can most easily see your DS being happy in, and otherwise keep doing what you're doing!
