You might also try fall seeding a small area to Cereal Rye. It has tremendous tolerance to cold, and will overwinter nearly anywhere. It is also great for generating biomass to create a mulch, and I think that its allelopathic properties are very underrated. It worked very well for us last year to hold down weeds, as Amaranthus species are some of our biggest problems. We have a lot of Tall Waterhemp, Redroot Pigweed, and some Palmer Amaranth- so you should definitely give it a try.