Oh good. I’ve been there with my DS (also diagnosed with ASD, lower functioning with other co morbidities). Like your child, he would fall asleep fine, in his own bed, on his own after a story. All in accordance with the ‘good sleep hygiene’ advice that I’d been given from our local sleep support group (heavily over subscribed, with little understanding of children with ASD).
And then he would wake anytime between 1am and 2:30am, and be awake and very active for about three hours sometimes more. He would go back to sleep for a couple of hours around the time that I needed to get up and get ready for work.
It was hellish. It changed my personality. I had little concentration, patience and dried at the drop of a hat. I worked out that he would sometimes (not every time) settle quicker if he came into our bed, had cuddles and reassurance. And even if he didn’t settle, that also allowed me to snooze a little as he was safe. Except that I was completely uncomfortable as he would lay entirely on top of me, not just a leg or an arm on top of me, his whole body laying on top of mine. I still managed to sleep, I was that tired.
After a couple of years of this, I bought a massive bed. And that changed everything as there is space for me, DH and DC (who now just cuddles up next to me and puts a leg on me, rather than his whole body). He goes to sleep later (about 9-10pm), and comes into us at about 2ish usually. And then settles pretty quickly and sleeps until 7am. I can’t believe that we have come so far.
The memories of being at the stage you are are very clear and I really sympathise. Please go back to the paediatrician and lay it all on the line with brutal honesty - you’re at breaking point and cannot cope another day as things are.