Another update since it's been a while and others might benefit from our experience.
We ended up enrolling our son in a private school for kids with behavioral problems. When we went to tour it the situation was a bit jarring. We could hear a kid raging out in a special room they have for such episodes; a couple of kids came up to us and just started talking to us about random stuff. They were nice, but it was socially awkward. That said, the administrator was great and when we toured the school our son really seemed at ease and liked it. At the end, uncharacteristically, he gave the administrator who gave us the tour a hug. His reaction to the school, our perception of it, their resources and professionalism and approach, plus our own research and conversations with other parents who either had their kids there or knew someone who did all led to us enrolling him. He started a few weeks into the fall semester last year. They told us that the first month or so was going to be tough, but that he would eventually get more comfortable. That is exactly what happened. He would do the same things he'd done before - cuss, scream, try to run out of the classroom, hit people - but the teachers were trained for this type of thing and all of the kids there were like that so they had a ton of experience dealing with it. They had basically perfected methods to address his exact types of behaviors. So even though at first his behavior wasn't better, the school was able and willing to deal with it and we didn't get calls or have to go pick him up or sit with him. It was a huge relief for my wife and me. The downside? Tuition is $40K/year. We made the decision that he would go to that school no matter what because it was so clearly what he needed. Our son even told us later that his life changed (for the better) when he started at the new school. Hearing that made all of the sacrifice worth it.
Fast forward. We got a recommendation from our pediatrician to take him to a pediatric neurologist. We did and they ordered some additional testing. The result? High-functioning autism. My wife cried when we got that diagnosis. I was surprised she did. After everything I had learned, I was expecting it and wasn't surprised or upset by it at all. If anything, I was relieved to get an even clearer picture of what my son has and how to deal with it. We've also changed his meds because the Abilify made him gain a lot of weight. So he's on low dosages of Lexapro and Vyvanse. His behavior overall is better, but he still has many, many episodes. He still melts down and cries and screams when things don't go a certain way. He still does socially unacceptable shit; mainly cussing. During the spring semester at the private school he showed strong progress, both behaviorally and academically. He was able to do more academic work and progress because he was trained by the teachers how to cope when he got frustrated. He's still behind, but he's made a lot of progress. He can read, but it's probably not at grade level.
Because of the cost of the school we had to sell our house and move to a smaller, less expensive house. I resisted that as long as we could, but ultimately it was the decision we had to make. It was still hard for me, but now that we've actually moved it's really not so bad. I've actually kind of enjoyed the change of scenery. Over time the lack of financial stress will also probably prove that the decision was totally worth it.
I guess the takeaway I would have for anyone starting to deal with this is that it has taken us A LONG time to get to a place, with a diagnosis and medication and the right school, where we can actually live our lives without total anxiety and misery. It's been like five years or so since all of this started.