[vacri]

> I have trouble rationalizing this romantic view of the homeless as these poor downtrodden, down on their luck people who just need a hand up, with the realities I see everyday of mentally ill, dangerous, and completely uncontrollable people.

Maybe you should see the demographic as being a little more complex rather than just throwing them all into the one bucket. Rather than 'find another term' to split the demographic itself ('homeless' is a pretty accurate description of 'doesn't have a home'), perhaps you should find a different term for the groups you want to specify.