How sad that your neighbor wants to get rid of them ! The tubers are so delicious. I grow them and every fall I cut them down then dig in and try to get as many tubers as I can find. I seem to always miss a few which is ok with me because then they'll regrow next year I guess if it's making her front yard a jungle I can understand I am growing mine on the side of my house and I don't really care how jungly it is. My bees seem to love the flowers. I'd go with trying to dig up as many tubers as you can because yum! (unless the herbicides have made them gross) I would hope the plastic would work, but with them being bulbs I'm not sure if it'll take care of them or not. I bet it'll take a few tries to get rid of all of it, maybe a mix of digging them up, plastic, and there's a herbicide for invasive plants like kudzoo? I used it on some ivy I just couldn't get rid of, that might work. Try spraying them then covering with the plastic.
