I have to agree with those who said that he is being overwhelmed by his senses. I think there is probably a lot going on here, but, a 13 year old Aspie KNOWS that he shouldn't be in diapers. He also knows that he shouldn't wet the bed. He can feel embarrassment just like any other teen! He is a teen boy, and many boys wet the bed at this age. My neurotypical husband wet the bed until he was 12. He needs to be out of diaper for sure! He also needs to learn how to respond to his body and recognize the sensations and feelings he is getting from it. This can be very difficult for any person, but those on the spectrum have a more difficult time.
We are using a massotage technique that is called Qigong. It is available online and at Amazon in a book that come with a DVD that tells you how to do it. It takes less than 20 minutes a day, that is with difficulty of fighting the child, but now, 6 weeks later, he comes up to us for his massage. Our son is 2.5, and the changes we have seen are amazing. I recommend that you look into this massage technique for you step-son. It will help him recognize what his body is saying, it will help with toe-walking, finger flapping, picking, and other "odd" behaviours. But, most importantly, it will help with toilet training! We haven't gotten there yet, but our guy isn't really old enough to even start training anyway.
I hope that with some new therapies and techniques, including an autism expert, you can get to what is going on with your son. I imagine that some Occupational Therapy maybe able to help him with his needs as well.
Your post was kind of confusing, but basically, we are hearing that he is getting sensory overload and that it is too much to process so his body is doing what it can, however it can. If you haven't done a lot of reading on it yet, look at Sensory Processing Disorder, and it might really help you understand what is going on inside his head when he get too many "rewards" or extra stimuli.
Also, the book Born on a Blue Day, is written by a high functioning Aspie that will really help you understand what it is like to think and feel and process so much so differently from the way we do as neurotypical people.
I wish you luck, and if I can help at all, please let me know! I can only imagine how tired and frustrated ALL of you are.