Ewwwww, tree type roots? I think you're doomed!
However, if it were me doing it, I think I'd line and overlap just the edges with heavy black plastic, then drape the landscape cloth over the whole thing (think lining a pool
), then lay rocks or bricks over the plastic and landscape cloth as an edging. I did something similar on an area in my front yard, where I have cottonwood trees and industrial strength weeds and grass, and it worked quite well!