Where I live in Georgia, our biggest invasive is the famous kudzu. Apparently young leaves, small
roots,etc are edible but its not very common for people to do so.
In my town there is an artist who's main "medium" is kudzu- he makes baskets, weavings , wall hangings, furniture, and all kinds of stuff out of it.
Sometimes I think finding uses for invasives just comes down to people experimenting.
Maybe kudzu fiber would make good paper or rope?