I
haven't tried it, but I think bamboo might have some potential. That is, of course, if you can control the spread of the bamboo.
I heard somewhere that u can get types of bamboo that dont put out runners and are easy to controll and if u cant find that kind u can get root barriers to stop the regular type from going too ballistic. Also there's this tree thing that keeps popping up in my yard that has leaves with a simmilar shape and colour too weed plants not shore of it name tho and im in australia so im not sure how much use that is too u guys exxcept sarah