Nutria problem

I live on a good sized pond in a neighborhood in Ascension that backs up to the forest. Been there nearly 4 years...but in the last year, I've been battling these things making holes in my backyard waters edge. I've got 2 traps and have tried on land and in water with sweet potatoes and carrots and can't seem to catch them, although my neighbor across the pond has trapped plenty this way and has even helped me rig. Been filling holes with quickrete which keeps them at bay for awhile then they come back. Luckily my yard slopes and my house is quite far from the waters edge. Trying to avoid spending thousands on a bulkhead. Would love to sit outside at midnight with a pellet gun but that isn't feasible. Driving me nuts, any suggestions?