I have numerous conervative family members, acquaintances, and friends. That comment proves one knows one's adversary remarkably well.
Historical and contemporary conservative approaches to homelessness tend to fixate on criminalization and enforcement: more cops to break up camps, more pretenses to jail homeless persons, more opportunities for the prison-industrial complex to get its cheap labor. "Jail the beggars, jail the addicts, jail the crazies." Today, a century ago, a millennium ago... the dynamics between the rich and poor are basically unchanged; all that's changed, at most, is how the rich get selected.
Are you saying that jailing the homeless wouldn't be popular with conservatives? I'm quite sure it actually is (although they prefer running them out of town because that's even cheaper.)
That's trivial; prison. (Ignoring the part where prisons now charge prisoners rent...)
Finding a solution everybody can agree on is much harder than finding a solution only one side or the other can agree with.