Welcome.
I agree with you and everybody. His environment needs to be tightened up. You can't chain him to his bed. He lies. Thwarts basic norms let alone laws.
The school performance is the least of it. That can be cleared up later.
I would do exactly as you say. Residential. There are programs for kids with mental illness diagnoses and learning disabilities. Wilderness programs...I don't know.
The other thing I would consider is teen challenge. There is one near me that is a working farm with animals, orchards, a pool, etc.
There are a number of kids here who are thriving in this environment. It is religious. That is one thing to consider. While I am not that religion I would have sent my kid in a heartbeat. Or at least I hope I would
I agree that he is incorrigible and requires an environment geared to containment.
What lies beneath this acting out might be complex. But first he needs to be contained.
Glad you are here with us. (But of course, sorry you have this on your plate.)