Thanks for taking the time to provide background data. This is all really great.
I'm skeptical of the percentages you shared, not because I think people are liars, but that rooting out causative effects is complex, especially in self-reported cases.
I have an aunt who was homeless for the better part of a decade. If you had spoken to her during this period of time about why she was homeless, she would have said many things such as (1) she lost her job (2) she got evicted (3) her family kicked her out. In reality she is a paranoid schizophrenic, who does not understand when she's not on her medication that she has schizophrenia. So, was she homeless because she lost her job? Yes. Did she lose her job because she was scaring customers due to her mental disorder? Yes.
When my father was in the hospital and detoxing from his alcohol abuse, he was asked repeatedly "Russ, do you have an alcohol problem?" He uniformly responded "No I do not." He only changed his tune when he believed answering in the affirmative would get his release.
My general point is that homelessness and substance abuse are deeply intertwined, and that if we pull on the thread long enough in someone's backstory, we'll often find that substance abuse was a catalyst in the chain reaction that resulted in their homelessness, but they aren't willing to, or aren't self aware enough, to recognize it.