From what you say, it is not really clear to me how many eggs they are eating. Are you getting any eggs, or are they eating them all? I ask because I occasionally see a hen eating an egg, but in my 8 years of chicken keeping, it has never become a persistent and widespread problem. After much observation, I have discovered that my hens will eat an egg if it accidentally breaks as they scuffle in and out of the next boxes. But they have not yet figured out that they can peck the eggs open themselves to get the goods. So I've never culled for this issue.