Nutria
The rules say one must prevent birds from eating the carcasses (maybe if the nutria were poisoned as a means of harvesting them), as all the State wants is the tails. So I see no reason one could not harvest these pest animals for their snakes, sans the use of poisons.
Nutria and Trade
One could freeze and sell the nutria. Traps would have to be used and no poisons could be used.