I'm pretty sure that if I had unlimited funds, I'd take the naive approach of fixing homelessness by building homes.

I'd design a mini-village for 5000 people, able to stand alone or surrounded by others. Then I'd build that, over and over again. I'd keep building as long as they kept coming.

I know this wouldn't solve the problem, but it would give those with a better handle on the situation more power to solve it.