First, start with the child psychologist. I am surprised you have had him tested for autism but not ADHD, because that's what leapt off the page to me. You could have been describing my kid -- extremely active, difficulty falling asleep and then staying asleep but up before the crack of dawn nevertheless, very bright, high difficulty sitting still, academic abilities a couple years ahead of her self-control, very impulsive, easily set off by loud noises/too-bright lights, distracted by tags/itchy clothes, etc. We got her official ADHD diagnosis at about 8, but in retrospect it was clear from about 2 on if we'd known what to look for. You have already read the best book (the one that got me through the terrible twos, which for her were 13 mos. to 3); I found 1-2-3 Magic to be a lifesaver by 4-5 yrs (because it forced us to act before we lost our temper, and boy did she pick up on our frustration even if we didn't say anything), but again, that won't help you so much with school. The things that helped us:
1. Melatonin. Kids cannot concentrate if they don't get enough sleep -- when you struggle to behave and stay on-task, it's hard enough when you've got a full belly and a solid night's sleep going for you; mess with any of those basics, and the cause is lost before you even had a chance. Can you go back to your sleep specialist? I've also heard Valerian is good but haven't tried it and don't know about side effects.
1.a. Routines/rules for when she couldn't sleep. I was very clear that she didn't have to be asleep, but she did have to be in her bed; if she couldn't sleep, she could turn her bedside light on and read. I figure at least it was calm, quiet time (side benefit that both my kids are voracious readers thanks to that early habit)!
2. As much running-around time outside as humanly possible before and after school. Schools are cutting recess and gym, even for little kids, and the first line of punishment for misbehavior is to take away the little recess that is left (talk about foot-shooting!). We chose a before- and after-care that threw the kids outside onto the playground for an hour before and after school. Walking won't do it -- it's running around like a dog chasing a squirrel. Kids like this have to exhaust themselves before they get to a point they can really maintain focus. Also, outside is best by far, even in crappy weather.
3. See if you can work with the teacher to implement some of the routines that work for you. For my kid, the best year was the teacher who had two ADHD kids herself -- she had these dividers that the kids could set up to work so they couldn't be distracted by the kids around her, she always used DD to run errands to the office for her or help take attendance, she'd assign DD jobs like sweeping the floor or cleaning the blackboards, etc. -- basically, she'd look for the signs of an impending meltdown and then divert that building energy into something useful that made DD feel like she was being grown-up and useful. Also, kids like this need to sit up front -- they have no filters, so all of the sounds from the classroom and movements from the other kids will pull their attention six ways from Sunday. The only chance the teacher has is to be the loudest voice that drowns out all the others.
4. Find small rewards that can be incentives for specific behaviors you want. Punishments don't work -- the kids already know they are different and "bad," and they are already frustrated as hell that they can't behave like a "good boy." More punishment from home can cement that "I'm a bad kid" really, really quickly. Also, target your goals very narrowly; "behave in class" is both far too vague a target and far too long a timeframe to work for this. You need to reward specific skills/things you want the kid to learn how to do that will teach him better alternatives than melting down. E.g., if he feels himself building toward losing it, he should raise his hand and ask the teacher if he may go to the bathroom (of course you need to tell the teacher about this plan first!!), and then jump up and down 50 times in the hallway on the way to/from the bathroom, so that he has a chance to distract himself and get that energy out. Or whatever might work for your kid. And any day that he does that behavior instead of melting down, he gets that treat (even if he melts down later -- you're not looking for perfection, you're looking to reinforce better habits, even when they don't immediately accomplish the desired end result). Put the dots really, really close together so he can succeed right away, and then make the requirements harder as he gets the easy ones under his belt -- you can even ask him to help figure out what he feels like when he is about to lose it, and to then brainstorm with you what some alternatives are. Anything can work, as long as it is inconsistent with melting down -- heck, there were times DD and I just sang incredibly silly songs, because you can't melt down when you're laughing.
5. Whatever you do, love him, snuggle him, and reaffim that he is a GOOD BOY. My DD ended up developing really bad anxiety and depression by the time we got her diagnosed, from just a few years of knowing she didn't fit in and not being able to meet the teachers' expectations and not really understanding why, and trying SO hard for so long, and still failing in the end, over and over again. It still makes me tear up to think how badly I failed her by not acting quickly enough, by seeing it as "behavior" that needed to be managed vs. how she was wired and something that I needed to teach her to work with -- that I and all her teachers were basically asking someone who is nearsighted to read the chalkboard from the far side of the room.
In the end, you might need to get an IEP to have the school work with the psychologist to get a formal plan in place. Or you might need to move him to private school (note: I would look for one where teachers are trained in these kinds of tactics and have smaller classes; some of the ones near us are really academic drill academy types that would be even worse for a kid like that). And if necessary, there are a variety of medications. But it's way, way too early to jump to any of that. Start with the psychologist and by working with the teacher. See if you can find patterns that set him off (like our post-school meltdowns), and then look for behaviors/distractions/alternatives that help him avoid the meltdown or calm down quickly when he does lose it (for DD, the soothing was rubbing her leg -- I always used to rub her leg to soothe her, and then she started doing that herself when she was upset). I bet you already know what many of those things are given your years of experience in figuring out your kid; all you need to do is figure out how to translate those to the classroom.