Christopher, I read about your problem with ground ivy. I have been using a spray called Crossbow from Dow AgriSciences that will kill any plant that has a woody stem, without killing any grasses. It was originally made for multi-flora roses, but I have used it on poison ivy, small sumac trees, and mulberry sprouts. If your ground ivy has a woody stem it should kill it - without harming any grass. We don't have any kudzu vines in Northern Indiana, but I believe it would kill that too.
I bought a gallon of this for $64 probably 20 years ago and still have about half of it left. A Google search says it is still available.
Erv Troyer Lagrange, IN