So, should I just let this go, or should I try triclopyr. I saw this interesting article by Ranger Dan:
Whatever kind of vine you have, there is a relatively non-toxic, earth-friendly herbicide (weed killer) called triclopyr. This is the technical name for the ingredient in many products. One product that is available to the homeowner is called "Vine-X", and it works for me. It contains vegetable oil, which makes the triclopyr penetrate bark, so all you have to do is paint it on (with the applicator bottle) to the bottom foot or so of the vines, and it kills the whole vine, roots and all. It's amazing. You don't have to go about spraying, with all the dangers of drift onto desireable vegetation and people. Triclopyr breaks down in the soil quickly, leaving no residue, and according to the online report on pesticide safety, it is virtually non-toxic to people and mammals. The U.S. Park Service uses it in combating alien plants, so you know it's environmentally benign. I work at a nature education facility, where we use it in wetlands. It is the herbicide of choice for use near water. I have been using a professional formulation called Pathfinder (basically the same formulation as Vine-X in bulk), and it has successfully killed the many invasive alien plants that I trunk-painted with it. It will kill even trees with trunks up to 6" in diameter, as well as most other vegetation except for most grasses, so you do need to be careful what it touches. Be careful not to get it onto any roots or leaves of anything you want to keep.