Hi, Other than physically digging each plant out (massively laborious), chemical control might be the right answer, if it is absolutely intolerable. Roundup is a compromise. It has a short residual and can be used near (not on) trees w/o damage. Folks restoring or creating prairies use roundup to eradicate non-natives, not because it's so safe, but because it serves the function well with a short residual. Not the answer that everyone wants to use, but we are still discovering how invasive some plants can become in certain situations. Digging is still the best answer. There are several species of plants that will not be touched by roundup and can be dug down to four feet deep and still return in spades (example- Fleece Flower). Lesson? Be very careful what you put where, do not underestimate a plants ability to take advantage of this ever-artificial environment.
Lisa, a professional weed-eradicator, in Mpls