Wow, it sounds like our kiddos are cut from the same cloth! My almost-four-year-old daughter has a provisional diagnosis of autism and exhibited (still does, but with therapy and special ed she is slowly making some improvement) a lot of the same behaviors as your son.
A lot of people have told me, "Oh, just lay off the potty training until she can communicate verbally that she has to go" or "Children with her sensory profile don't train until they are seven or eight." Do NOT listen to them. Definitely talk with his therapists and get a plan of action in place. Your son might take to it immediately, but if not, brace yourself to be content with patient progress.
Our experience toilet training can be summed up in three words: routine, routine, routine. I have tried every known method over the past year and a half for both communication-delayed and typically-developing children, and nothing else works. I still do a lot of laundry around here, and our couch pretty much needs replacement, but the payoff has been worth it. My daughter has developed significant bladder control, has consecutive dry days here and there, and is slowly becoming more comfortable using public toilets. Like I said, it's not perfect, but until the time that she can do this independently, this will do.
Oh, and get rid of the Pull-ups. Every time I backpedaled on that for convenience's sake it set us back. Go to Target and buy Gerber padded cotton training pants. If you're going somewhere where you're nervous about him having an accident, have him wear vinyl underpants on top of them. Additionally, involve him in the clean-up process. I have my kid take her pee-pee panties off and put them in the "yucky bucket" (a bucket we keep next to the washer for this purpose). If there's pee on the floor, I give her a paper towel and we sing the clean-up song.
I hope this is helpful. Best of luck to you and your son.