Nah, I think special diets are only effective for kids with allergies or nutritional deficit/imbalances/special needs. I've not heard of any diet that cures a neuro disorder. I think eating well can help all of our brains function properly and I think if that's not happening, it can sure exacerbate underlying issues, or mimic others.
I hear you about feeling exhausted and exasperated though. That sounds like a tough place to be in mama, and I can relate to feeling like I'm out of options and at my wits end.
I wanted to offer one suggestion, that I got off a mama on the beach. Her little one was about the age of mine, and she'd just gotten back from a convention for parents of autistic kids. I don't know if you'd already tried that with your kiddo, but she told me it really helped her daughter when she drew out pictures before an activity.
For example, let's say she needed to get her daughter to brush her teeth, put on clothes, socks, and shoes, eat breakfast, and then walk outside to the car so they could go to the doctors. Well, she'd draw out stick figures illustrating each point. First there would be a little stick figure brushing her teeth, the putting on clothes, then socks.
I started doing that on some of our more difficult days and it helped a lot (she's got different stuff going on, but I like to grab from all the toolboxes I can find). I find it's also really useful in explaining difficult concepts, or emotionally weighted subjects. She can really relate and prepare, when she has a visual aid.
I also wanted to ask you a question. Do you have an ability to take a break and leave your house for a few hours every week? Just you time to relax, catch up on chores, make a phone call, or take a too hot bath? I parent a very challenging kiddo and I've got to be honest, without taking time out away from my kids I would snap. Since we can't afford a babysitter, I set up trades with a few of my mom friends. One of the boys I trade with, sounds quite a lot like your son, down to the potty training stuff (no leaking though on their end, so probably not as taxing). It's really helpful for both of us. She usually crafts and I usually go out for coffee.
Anyway, I really wish you the best of luck and big hugs. I hope you find the answers that you are looking for.