Instead of a homeless shelter, how about more actual affordable housing? So people can get out of the shelters and off the streets.
In North St Louis they tore down the projects that were hud and forced families to move to North St Louis county aka Spanish Lake and Ferguson etc and built HUD apartments there.
Maybe what you want is basic income to live on and afford housing and food, etc?
Though I am curious as to what you think of as "affordable" in Seattle. Care to provide some examples?