I use that extra strength Poisen Ivy Brush Killer from Lowes on anything I want to kill that has runners. Black Locust trees, some other trees that have wild runners, etc. I spray it on the leaves to aborb, and also cut slits along the bark with a sharp knife to open wounds to absorb more poisen. it will get down into the roots it seems and kill off a big portion of the plant, if not all of it. Guess just be careful and make sure no fruits/veggies close by to spray onto. Doubt the roots would 'cross' and spread to other plants. I never had that issue as Im careful not to spray on a windy day. You might be able to cut up the plant now and spray the just bark when its waking up. Not sure whats more effective in that regard.

You can use one of those foam paint brushes, dip it in the solution and brush it on the plant without worry of drips and getting it on anything but the target plant. Good luck!

Thanks everyone!! I will try that with the brush idea. I also have a giant jade plant strangling one of the rose bushes I do want to keep (WHY? WHY plant those two 3 inches apart?!). I'll try the same method on that beastly stump, too.