I threw a couple golf balls in the box and sealed up the air gaps to try to make it darker. And my problem has disappeared so far.
I have read stuff suggesting that eating eggs may be a protien deficiency.
Oh no, that’s definitely a problem! Identifying the culprit would help greatly. Birds will learn to eat eggs from each other, so finding the culprit and separating her from the group will prevent the rest of your hens from starting this habit.
Since you are having difficulty finding the culprit, there are other steps that you can take to try to break your hens of this habit. First, collect those eggs as often as you can. The longer they stay in the coop, the more likely something bad will happen to them. Other options are to place wooden or ceramic eggs (people have even used golf balls) in the nest boxes. The hens can’t break these open, so they begin to lose interest in trying.
Another suggestion that people have tried is to take an egg and blow out its contents. Make a small hole in one end and a slightly larger hole in the other and blow the contents of the egg out of the egg. Next, fill the egg with mustard and seal the holes (or leave them open depending on how much mustard you used). Place the mustard egg in the nest box. When the hens destroy this egg, they get a beak full of mustard. They don’t enjoy the taste of mustard as much as they do an egg, so they learn to leave the eggs alone. You may need to do this over several days until they stop breaking the eggs.