Another resource might be to join a neurodiversity board to ask others on there what their experience with the medication has been. Based on the topics I've seen, there have been very mixed results, but ADHD meds do tend to cause weird reactions for Aspies unless they are co-morbid ADHD.
If he's stimming the way you describe and has the gross motor deficiencies, I personally would lean more toward Aspie than ADHD (being aspie myself), but you should definitely find a professional to diagnose and not rely on a pediatrician at all. There are very few people who have had any luck with their PCP noticing autism traits or even believing a confirmed diagnosis. It can be especially more difficult to pick up on in gifted people.
