Everyone who wants to climb Everest pays in 100 bucks to register. Winner has to pony up another 900 for the permit, and fines for leaving material on the mountain. Spend the net profit on cleaning up after the people who already left shit on the mountain.
But here's another alternative that also fixes it:
To get a permit to climb Everest, you have to have spent some hundreds of hours volunteering for the crew doing cleanup. You'd see the lower 70% of the route multiple times before it was ever your turn. You'll get a hint of how you respond to altitude + cold. You'll understand what a flying pain in the ass it is to clean up after asshole climbers. You will also go farther up Everest than most people ever will, and you'll be reducing the human footprint in the process.