The way it's described as horribly rampant an a "nemesis" sounds like Oriental bittersweet. Yes, that is used for ornamental wreaths, but the problem is if that the poor recipient of the charming ornamental wreath is a good girl and throws it in her
compost heap after the season ends, and now you've shared your invasive problem with her, not only your wreath.
My
experience is that bittersweet is very hard to eradicate completely but if you pull up as much of the (distinctively orange)
root as you can, you can seriously weaken it, so that if you do this once or twice a year you can keep it from climbing over and killing your
trees. Of
course conventional websites say to treat it with topical herbicide such as Round-Up, in order to kill more of the root, but I'm not willing to do that, especially since I'm pulling it out from under beloved trees.
I'm wondering if a topical treatment of the fresh stump with vinegar might help weaken the root a bit? I understand that vinegar gets digested by the environment, unlike salt, which will ruin the soil for future plants.