When my son was going through this (he is 3) I had to do the Candida diet, totally wiped him of all foods, dairy, carbs, fruits, and he also likes the same stuff your son does. It was not easy, he ate nothing pretty much the first few days and the transition took some time but I made him lots of homemade carb look-alike products. I looked up Candida recipes and had to make everything from scratch, my son ended up really enjoying the homemade muffins, the cinnamon and lemon flavored foods. Homemade pancakes of coconut flour and buckwheat with Agave syrup. It took three months but he got use to the diet and he was going potty regularly. Now I am not one of those healthnut moms, but my son was in pain and constantly going to the bathroom and sometimes nothing would even come out. After three months of this diet I slowly introduced his favorite foods back in and faded out the homemade stuff (as its a lot of work). I added some fruits back in and vegs first so I could get him to eat more of that food. He was so excited to see new kinds of food that he now loves edamame and carrots as before the diet he never touched any of it. Then I weaned him onto the carbs and a bit healthier choices, kinda like how you wean a baby onto new solid foods. Now, he eats greek yogurt daily and his stomach is sooooo much better. If he has an issue that arises with constipation I give him sandwiches with peanut butter and puree prune spread for a few days and he is back to doing well. To be honest I have only done the prune sandwiches once since he has been back on this diet and its been a year since the cleanse.
I am also an Aspie so I apologize for my details and ramblings on. I hope I have been of help. I really hope you consider it. Its for yeast build up but it is also a good system cleans that is natrual. Just know their will be a week of a form of "detox" from all the carbs so prepare for tantrums times 2! Just be patient with him and know what he is going through is not fun and he can not help it. It may seem like a lot of trouble but if he is as bad as my baby was getting, I highly recommend the trouble it may cause in the beginning. Good luck and give him hugs
I hope he gets help.
p.s- my sister was recently diagnosed with colitis. She was running to the bathroom often as well, maybe ask your doctor to do a colonoscopy if you have further concerns.