I think looking at the book Diagnosis and Dual Diagnosis of Gifted Children and Adults by James Webb et al might be helpful to you-- there are definite overlaps between how gifted children and children with ASD might behave, but there are some very specific ways in which they differ too (which the book lays out). It might help you pin point your specific concerns and decide whether or not you think the evaluation you got was a good one. Did they do the ADOS? What about ADD testing? (The focus thing makes me think of that-- ) The "overexcitabilities" that gifted kids have can look a lot like diagnostic criteria for ASD, ADD, OCD, you name it-- and they can be several things, of course. Additionally, reading early is not in and of itself a sign of ASD, at all-- see this article linked below:

https://www.wisconsinmedicalsociety...-reading-precociousness-or-savant-skill/

If you do decide to do more testing, I might consider seeing a PT (not being able to tie shoes or ride a bike or having trouble with handwriting can be just a matter of muscle tone). That can help with anxiety too, if he's feeling uncertain in his body.