Thinking more about this, and again, I doubt if anything organic will kill it. Oh, you''l keep it at bay for a little while, but it'll be back. A guy down the street from me had a HUGE patch of it. He cut it down with a sickle bar, then covered it all over with heavy black plastic, staked it down then mulched over it about 6"with wood chips. A month later, the evil stuff had poked through the plastic and chips, and was happily taking the area over again.
There are some things you are nice with, and use a kind, gentle approach. Other things, like japanese knotweed, you take off the gloves and use everything short of a nuke to take it out. You either use pesticides, and strong ones, or learn to like knotweed.