In nearly every study ever done physical punishment is linked with worse outcomes. It may "work" in that it frightens younger children into hiding things better as not to experience physical punishment, but it teaches nothing, especially not coping mechanisms or anything useful for the child except avoidance.. Im not saying that as some sort of anti spanking Nazi; when my daughter was younger a well timed swat to make a point happened more than once. But for an older child with behavioral issues, especially with an unknown past experience and possible predisposition to mental health problems, physical punishment sounds llike the very worst idea and would likely make his behavior and mental health worse, not better. And thats not my opinion, that is scientifically upheld fact. Yes, it does appear to be on a scale, ie harsher punishment causes worse issues etc, but with an unknown past, its better not to play roulette with gene and environment interplays, in my opinion.
https://www.aap.org/en-us/about-the-aap/aap-press-room/pages/Spanking-Linked-to-Mental-Illness.aspx
Your point about dynamics,though, is a solid one. Changing them can be helpful. Most of my mental health treatment experience is with adults, but one of my youngest patients was a young teenager with mostly behavioral issues. She was out of control, was kicked out of school, had violent behavior very similar to that described by the OP. She responded really well to simplfying her life (ie her parents took away nearly everything but a change of clothes and a pillow/blanket) and she earned things back with an elaborate chart developed with her parents and treatment team (it included everything from daily responsibilities to handling things appropriately and was no doubt an intense project for her parents). It gave her something to work for, and was a long enough process (over months) that she was able to learn self regulation and other skills along the way. This time did include inpatient treatment in a mental health unit (where I met her and upheld her chart while she was there) and they did get her on a useful med as well as involved her in groups where she could start to learn skills like delayed gratification, anger management and how to communicate your needs to people in a clear and non violent way. Many people that advocate punishment only dont really understand that often learning these skills are the difference between someone who is totally disabled with their mental disorder and someone who can manage, even in severe cases like schizophrenia. It sounds silly, like its something "average" kids learn through life, but sometimes it takes targeted learning and treatment, a tutor if you will, to help people who are not average grasp these things.
OP, I am sorry there arent more resources for you in this area. Our drug and dump mental health treatment is sad and doesn't help anyone. and I don't envy the amount of work it takes to get a child like that on track, its HARD. But you dont have to do it alone! Please find a good support group , even online forums and make sure you are taken care of as well. My father has late stage cancer and we found a WEALTH of knowledge online from other families, things that helped not only with his treatment, but with his comfort as well. Tapping in to that has made all of the "stuff" such so much easier to navigate. Best of luck, adn whatever you need to do to be safe and provide a chance for hima nd your family is the right decision.

Good post!