I know that my 5.5 yr old son (has been potty trained since 4) will hold his poop. Sometimes, he will hold it so hard that it will cause him to wet on himself. I think he just doesn't really like the sensation of going poop. But, I make sure that he eats lots of fruits and veggies and fiber and I suggest that he sit on the toilet at least once a day to go so that he stays regular. I can tell that he is feeling a little out of it when he is constipated. So I think this might be why your son is acting more "stimmy" when he has to go. He is probably dreading it, and trying to postpone it. I would suggest trying to stay really in tune with this and work on getting him trained. Even if you have to physically walk him to the potty.
Also, the sleep issues are definitely something to work on. Try getting him into a really good night time routine. Do things that are relaxing and soothing. Such as music, a nice warm bath, reading him a story. Try to keep his bedtime the same. Also, I have heard that melatonin can help with sleep.
I know that every case of autism is different, but I have never done anything biomedical with my son. Other than doing my best to make sure he is eating a balanced diet, (which I know can be difficult for some autistics) And giving him a multi vitamin and a fishoil. And doing lots of occupational, speech and physical therapy.
As far as his speech goes, just spending time with him, playing, reading to him, talking to him, may help. But I think helping him to feel better will be the first step in making some progress.
I know this has to be very tough, but just keep trying to find what it is that will reach your son.
Best of luck to you and your son.