Critter - the only other green method for weed removal that I haven't seen mentioned is to mulch it out of existence. If you cut it off at the ground and lay a very heavy layer of papers, cardboard, black plastic that can be removed, etc over it, it will eventually give up. If the 3 foot space gets lots of sunshine, black plastic will work the fastest. Good luck, girl. You have taken on a mighty task.
Be sure to let us know what you decide to do and how it works out. We're all ears!