Wiping this out would be a major and multiple year endeavor. I suggest cutting off and covering with heavy duty black plastic and then planting in containers over this area, especially for perennials. This way you will be able to take any plants you wish with you when you move without bringing chunks of knotweed to your new situation.
Another approach would be strawbale beds (with same barrier to prevent the knotweed coming up through). They are watered to begin the decomposition process (preferably with an organic fish-kelp or urine) and then topped with about 3 inches of topsoil. I am using some for plants that can't tolerate the black walnut phytotoxins in proximity to my garden in rented location. If you get bales that are tightly tied with plastic twine (or tie them with a non-decomposing rope yourself), you don't even need any other container. Now I can grow tomatoes and peppers!
