If rooster approach used, then something really big like Jersey Giant or Siapans would be my first choice. Potential problem with roosters is with mine (game roosters) which can be really good only operate in social groups involving harems and the roosters only do a good job from About now...
You are having similar problems I had. Your dogs are likely too spread out or cannot cover the whole area. I had to increase number of dogs. We also have roosters that do work on hawks from cover. The cover approach I use would likely not be effective in a commercial setting.
At home my dogs...