I’m sorry you are going through this. I know that everyone always wants to find the hidden reason and some kind of “fix it” solution. Ultimately I’m not sure it matters. The horse isn’t safe the way he is now and I don’t think it’s worth risking serious injury (of yourself or anyone else) to test out whether or not any possible “solution” has worked.
The unpredictable nature of the behavior adds to the danger. A horse that has a consistent quirk can be managed. I once had a rearer that I considered “safe” because his triggers for rearing were predictable, he always gave some warning before doing it, and the behavior could be avoided by following a simple routine. On the other hand, a horse that has a surprise behavior like a bronc worthy bucking fit 1% of the time with no warning or identifiable trigger is extremely dangerous.
FWIW, I relate to your post on a personal level. I imported a gorgeous young horse some years back. She was raised with ideal handling and training and had excellent ground manners. Her early training was with skilled professionals and no corners were cut, but when I took over the ride (and I have started and trained more young horses than I can recount) she started out lovely–relaxed, attentive, steady…and then wham, out of nowhere a nasty bucking fit. It didn’t make sense, but I assumed there was a hole in her training that we would figure out. Extensive vet work revealed nothing.
Three different trainers tried to work with her, all three with a ton of experience, the second one a pretty tough cowboy, and I ended up giving (for free) the horse to the third trainer, another extremely experienced person with all the facilities for a tough horse. They all had the same experience–a horse that was reasonable and lovely, until out of the blue she turned into a bronc. I strongly regret giving the horse away. I knew she was dangerous and I should have euthanized her myself instead of putting someone else at risk. The third trainer sustained a fall that could have been devastating. At that point she called me up and we both agreed the horse should be euthanized, recognizing there was no safe way to re-home her, someone would always be thinking they could ride her and she was just too dangerous.
I think it is hard to re-home a horse in a manner that can guarantee that a horse will never be ridden. I’m skeptical about donating to a university program despite @Xctrygirl 's experience. All it would take is some staff turnover for you to potentially lose track of the situation. Universities do send horses to auction, and I think that communication with a program can be quite variable.