The solution, at least for the "harmless homeless" is to credibly broadcast to civilians and authorities their benign circumstances and histories. With widespread facial recognition and augmented reality, this might not be as hard to do as it seems. The homeless can be assigned a social credit score based on their criminal record, user rating by shelters and other provider institutions, employment history, and how long they've been homeless. Authorities, and potentially even civilians, can instantly identify and flag homeless people that are likely to be problematic.
Without a doubt, this regime would certainly make life better for the harmless and down-on-their-luck homeless types. Yet my guess is most would oppose such a system. The point is tradeoffs exist in the social design space. Most of the down-on-the-luck homeless are unfairly stigmatized because society at large lumps them in with the violent, destructive and anti-social. We can make more efforts to draw a visible class distinction between those respective groups, yet it's often homeless advocates that oppose doing so.