I never worked with ACT. Not sure what it is.
Does your son get Disability,? If so, he has a case manager even if he doesn't use the case manager. I am thinking that you can try calling his Case Manager, who probably has connections. If your son is not already on SSDI, it would help him and maybe help you too. They also try to get housing for the disabled and my nephew only pays 1/3 of his income for hos apartment, electricity and heat. Most of his salary is his SSDI monthly payment. Very doable. Nephew lives in a fairly nice apartment complex for disabled adults and it has been a Godsend. However....there was a waiting list. He paid for an inexpensive studio apartment until he could get in.
I am not sure it ever goes really fast. But you can try his case manager.
This is also important. Most places have rules that you have to follow. If he is incapable of following rules, I assume it is much harder to find a place. Patience. (Easier said than done but it is often necessary).
Keep us updated. Sending prayers.