Pay those who collect cans to pickup trash

YES- I think this would work. There are those that can turn this trash problem into income, and those are the people you want to get on board. They are motivated and will do the work that no one else wants to. This solution just needs to be coupled with a way for them to dispose of the trash they pick up. It can be like a recycling center, but a recycling and trash collection center where they can be paid out.