I had a terrible infestation of the invasive vine, bittersweet. The only way to eradicate the bittersweet vines are to cut them to a few inches above ground, and then using an eye dropper, or other means, place several drops of glyphosate directly on the top of the cut portion. (Similar to the wet rag and plastic bag mentioned) Out of over 350 vines, only 10-15 grew back. Each year, twice a year, I find them, cut them, and kill them. The berries are carried by birds, so I could be getting neighborhood plants dropped on my property. But, after trying everything else, this is the only thing that works. You can buy a bottle of straight glyphosate at walmart or home depot around here. Worth the time and money for me, so I hope it helps as much for your situation.