We are not homeschooling ... yet! But I am pretty sure we are heading down that direction (DS4.9 and DS3.2). I know all the behavior issues sound scary but I would certainly give it a try. Once your son realizes that he'll be spending a lot less time doing school work since a lot more can be accomplished with a one-on-one schooling rather than trying to get through the school day and homeschool on top of that, he might start to appreciate it more and behave better. I can't imagine public school being fun for him so just time time thing alone might be a great motivation for him and once he sees more progress he might get a lot more excited about learning.
I can relate on the "special school" front. DS3.2 has a high functioning autism diagnosis. The Psychiatrist said he should be ok in a regular classroom, maybe needing an aid. Yet when he started therapies in the school setting, he completely checked out, is completely non-compliant, angry ... in just 5 weeks of twice weekly therapy it has gotten so bad I pulled him out as of yesterday. The way he acts at school the therapists basically told us they can't imagine him functioning in a regular classroom. He would need to go to an all autistic class where they concentrate on behavior and basic life skills. There is absolutely NO WAY we would agree with any of that. Aside from the fact that this would be exactly the thing that he can't stand, we are not going to put a child that started reading and doing math at 2.5 years old, is starting to spell, understands quite complex contexts just by looking at them into a class where the main focus will be breaking his behavior? Especially when this behavior only really comes into play when he's at school? At home and other non-stressful places he acts quite close to normal. So, needless to say, we are determined to make it work financially and homeschool if we find it necessary. Plus DS4.9 would likely benefit from homeschooling as well. So while I can't relate to your son's "dys-" issues, I can certainly relate overall

And you can always just try it and if it doesn't work out, there is always a public school system to go back to!