Why can’t we set up a bank of storage lockers, where people could pay a nominal fee by the week to keep their personal items safe?  Maybe in the parking lot of Beans cafe, or something? 
Then why not set up some public showers similar to Seward Harbor Master where anyone could go and pay a couple of bucks for a shower when they were so inclined?  Would not totally mitigate these problems, but would likely give homeless people a slightly better situation, and both of these things would be self-supporting...