The most important things to do are, increase the protein in their diet. Treats like dry cat food and black oil sunflower seeds are around 30% and that will make a world a difference. They are lacking enough protein and are smart enough to find what they need in the eggs because of their high protein content.
Darken the nests by placing a sheet accross the front and cutting a slit for the entrance. Hens can't eat eggs they can't see. They will still enter to lay and have more privacy. Egg eaters teach others to do the same, so this needs attention and I know these things help alot. Even though commercial feed is suppose to have everything needed, stressful hens require more protein to stay healthy. Collect eggs often as possible to also help keep them from pecking at them. Good Luck.
bigzio