Looking at the pics, I'd remove the chainlink fence, practice a minor scorched earth attack along the problem area & once every is dead plant something agreeable.
^^^
I would go this route. It's ez to do. Less chemicals.
If you don't like the vines, just remove the fence, and pull up the vine then put the fence back... It's easy to do. You can use 2 or 3 large harbor freight C-Clamp as a stretcher... or any Bar-clamp etc...
Just go to a fence store or lowes and buy minimal needed supply like the aluminum ties.
