Have you seen the new TV show "Rat Bastards"? Nutria hunting for $15/head bounty. Some real winners there.
The nutria were a lot more confrontational than I expected. Maybe they were playing up that aspect, but I didn't blame the guy using the (I think) 12-gauge. Slogging through the swamp to find them doesn't sound like a lot of fun, I think I'd probably sit for a while and see if they come out like the woodchucks do up north.