There is a LOT more to a humane kill than simple marksmanship. Even an perfect "double lung" shot does not guarantee recovery. Its a sad aspect of hunting. ANY hunter who does not feel horrible for not finding an animal they shoot, is not a true hunter who does it out of respect for the wild.
FWIW, any broadside shot in the torso, using modern hunting rifle ammo, should result in a relativley humane kill.
I don't know about IN, but in PA... When they do these "cull" hunts, they require a marksmanship test. Also, FWIW, I personally would not participate in such a hunt. Yes, it is required to be done. This kind of control is better than starvation or CWD... But its not a "hunt". Big difference between a "cull" and hunting.