Your situation is so difficult. No matter what any of us choose to do to help our loved family members with sz, something can go wrong. That said, my opinion is that I do not think you should give him $6,600.00 directly.
I feel you have correctly identified the crux of the problem: homeless in autumn/ winter or the possibility of illness lasting longer. I hate to write this third possibility: if he received the money, are you sure he would use it for what he says it would be used for? If there is any chance he is using illicit substances to self medicate, you don’t want to hand him the money for more.
If you don’t give his current landlord that money, maybe he gets kicked out of that place, but you could help him with a different place? One that is found through services at a homeless shelter might be less expensive and more supportive?
I think the course will help you in the short and long run.
I’m really glad your son is okay. Sounds like he has enough coping mechanisms and inner resources to get through this, even if he is evicted.