I can’t claim to be an expert on either autism or different dog breeds’ reactions to it, even though I have had and transported many dogs previously unknown to me and, have 3 grandchildren in one family all of whom are autistic to differing degrees. They do not have a dog because one of the boys is terrified of them.
But what I do know is that, although there are skills and behaviours prevalent in some breeds rather than others, and autistic behaviours quite different in different people, as a general rule there is no better way than ‘suck it and see’. I do not know how old you are Caroline, but as a general rule I prefer puppies to not be adopted by older people and also, from bitter experience am not enamoured of breeders either.
My only advice would be to take your son to visit dogs in a rehoming centre like the SPA, or find a reputable charity which rehomes dogs, like Phoenix in the Dordogne. Often the dogs will be in a home environment with fosterers who will know first hand if their charge is suitable in your situation. On that score you could foster yourself for a time and adopt or return according to experience gained.
Lastly, I would advise putting out of your mind any fixation on particular breeds, often the mixture in cross breeds is beneficial in terms of behaviour and health (of the dog), and no-one should rule out breeds on reputation alone. The dog of mine, Boss the Rottweiler, whose photo you admired recently, would have been ideal for your son as he was so gentle and immune to bad bahaviour in others, both canine and human. He was kept as a scrap yard dog in Spain for some years and then discarded without any attempt at rehoming when no longer required. Badly treated by humans he ended in a refuge near Paris and I went to meet him. Down on my knees, at his level, and on a short lead, he marched straight into my arms in a massive hug. By the time we got home the next day he was no longer a foster and the papers were on their way. He was the same with dogs. Mid transport from the Alps to Brittany, I had to keep over the weekend a female Dobermann at our house. In the garden I let Boss walk freely and approached him with the Dobie on a lead. Her teeth came on display and she lunged straight at him, only prevented from making contact by me and the lead. He stood his ground and just looked at her it seemed with sadness more than anything else. The next day, with the help of a friend, I walked the 2 of them on leads together but just enough distance to avoid physical contact between them. After 15 minutes and back in the garden both of them were free and totally comfortable in each other’s presence. If she hadn’t already been adopted I would have considered fostering, and maybe adopting, her.
I relate that not to advise a Rottie, or any other so-called ‘dangerous’ breed but to demonstrate that it is the dog, not the breed which matters. Indeed, I wouldn’t recommend a dangerous breed simply because of the moronic hoops you have to jump through and vast expense you will be put to in obeying the regulations.
Best of luck, I do hope you find the perfect answer for the 3 of you. 