The staff in public schools are not qualified to make a medical diagnosis. They will very often miss Asperger's or Autism in a bright child.
With the behaviors you describe, I'd go to a private practitioner (psychologist, neuropsych, or developmental pediatrician) who has a lot of experience with kids with autism, and get a thorough private evaluation. This will give you better information about how to proceed. If the issue is that you also need services (PT/OT/speech) from the school, you can take this info back to the school to persuade them to reopen the case and evaluate again.
You say "no rush"-- but if he's flipping out all the time, he may be under a lot of stress. If there's a chance of alleviating some of that stress, I probably would want to do that.
