This problem isn't going away.  So, one day in Eugene, and elsewhere, this is what will happen.
 
Public parks and other public areas (including streets and sidewalks) will be off-limits to anyone wishing to camp or to store their belongings.  This applies to everyone--you, me, everyone.  That's the purpose of a public park and a public area:  on one gets to live there.  If you can't do that--if you can't at least enforce the basic, actual purpose of the public area--you can't do "public" anything.

When anyone attempts to live or store their belongings in a public area, they will immediately be forcefully transported to a designated area in which they are permitted to live, camp, and store their belongings.  The quality of this area will be as determined by the local jurisdiction, and the local voters and taxpayers.

Homeless advocates can volunteer at this area, and make financial contributions, as they see fit.