Good idea, with one small change: bring the dogs in alive. That way they can be euthanised in a nice way (painless and quick), and not by locals trying to drown them or hitting them with a shovel. Just let them lure the dogs with some food.
After that one month the local government can employ dog catchers to keep the soi dog population close to zero. If you see a dog wandering around, you call them and they come pick it up. Next also hire some "animal police" who can be called for people not taking decent care of their dog or for letting the dogs out of the front gate alone.