Adding mulch, tree trimmings, leaves and chips only serve to fertilize and help the unwanted plants to grow stronger.
Long term effects of glyphosate:
http://www.motherjones.com/tom...
I can't begin to imagine how big a job it will be to cover such a large area with cardboard but I will stand here and applaud you for not using chemicals.
You could contact major appliance retailers and ask to pick up the cardboard before they send it to recycling. You could contact the recycling companies to see if they would cooperate and let you have some. I once had to move a 4 x 8 piece of material during a high wind so I would say...check the wind report before you begin the project and take it one section at a time. Slow and steady; doesn't have to be completed in one go.
Don't forget that heavy plastic can also work to solarize/kill the unwanted plants. Good luck!
