Would it be possible to eat our way out of a species invasion? Kudzu, for instance. The Asian vine has taken over to such an extent that it's hard to think about a Southern landscape without imagining telephone poles, old barns, hillsides, trees, slow-moving cows covered in the thick, rich, green drapery of kudzu.
Here's a list of kudzu-related sites, including some with recipes. I've never eaten the stuff, but I'd be willing to try.
I wonder if any other invasive species have become this incorporated into the culture and tradition of the regions they infest? Oh yeah . . . Kentucky bluegrass.