This. Your child needs to be evaluated by a psychiatrist and put on medication that is appropriate to his diagnosis. You wouldn’t give supplements and herbals (which are unregulated, by the way) for diabetes and then wonder why he’s in a coma.
A thorough outpatient evaluation by a board-certified child & adolescent psychiatrist seems to be in order. Certainly, this would be the way to go before jumping to a therapeutic boarding school.
Have any of the professionals he’s seen ruled out bipolar disorder? It presents very differently in children than in adults.