No matter how well fed chickens are always starving when you bring in more food even if it's what is in the feeder. When you refill their feeder if they get aggressive take your finger and peck the most aggressive one on top of the head once or twice and work your way down the list till they quit. The big dog in the coop doesn't put up with that kind id behavior and this they understand. You never see a hen pecking on the top rooster at least not for long. Some hens may still peck at things to check them out because that is how they learn about things but aggressive behavior should not be allowed.
The pushing away probably won"t stop them if you'll watch your girls when they all want to eat you'll see the hens pushing their way in to the food.The girls that get pushed aside don't just give up they circle and attack from a different angle, their used to this as normal but a peck on the head gets their attention. If you do this tho you have to mean it a little push peck won't even phase them. I'm not saying to hurt them but get their attention and let them know you mean business. Just one quick peck and ignore them if they quit, you've made your point.