Michelle-- I understand you do not want to use round-up, and I support that. I am going to explain it first and then maybe brainstorm to substitute. You take 5 gallon buckets or trash cans, pull the vines and make sure the lead/top of the vine is cut open and put the vines in the bottom, anchor the vines in stones or bricks, pour round-up in (We need to find a substitute for this step) cover so animals do not get in. Let it sit at least a week. You want the entire vine to drink it. So we need something for it to drink. First off I am thinking hot boiling water to start, maybe if you have a propane heater. Salt could be added to it, maybe let it evaporate as you are doing this so you do not have to pour the salt water anywhere. Something else could be a commercially available stronger chlorine to add, pretty quickly the sun eats the chlorine so you would not have to deal with disposal of that. I am sure there are other options and someone else could give us some ideas along this route of getting whole vines. Many blessings to you and your family!