I broke my egg-eaters by simply spending a whole lot of time with them and disciplining them when they showed interest in eggs. Chickens "disagree" with one another by pecking, and if something is REALLY wrong they'll bite the back of the offender's neck and push the head to the ground, holding them there until they relax. The key to that is that you MUST wait until they have RELAXED. Not when they stop struggling, but when their muscles release all the tension and they relax. Also, just holding the head down can hurt the chicken if they struggle, so you may want to place one hand on their back to restrain them from jumping around and hurting themselves, but DO NOT put too much pressure on their backs / chests. Birds do not have diaphragms, so they must use their entire chest cavity to expand and contract their lungs to breathe, so if you restrain TOO MUCH it can suffocate them.
My girls would eat their eggs because they were bored, which is really the leading cause of egg-eating. They're bored and don't have anything to play with or occupy themselves with ( and free ranging isn't an all-engaging activity - chickens do more than eat and forage, and sometimes they'll just want to explore or play ), but they have this egg to peck at and roll around. I've seen a video of roosters playing soccer ( with a bunny, at that! ), and chickens playing with cat toys that are a ball on a spring that hangs from a verticle stick that's stuck into a base ( kind of like a springy may pole ), and there's even
chicken agility and obstacle courses!
To keep my girls occupied I rolled up bits of newspaper and gave it to them to play with, and took them out on trips often. I've trained my chickens to ride the handlebars of my bike, and for the chickens that aren't as comfortable on handle bars I have a belly-bag for them. They LOVE bike rides and seeing new places and meeting new people. They bask in the attention they get when I bring them into the city. They'll even start making a fuss when I haven't taken them out recently enough. My roosters are so happy they hardly ever crow, and when they do they're trying to tell me that I haven't paid them enough mind recently! So long as I keep them occupied and feeling safe, my chickens are pretty quiet.
To keep them from eating their eggs, I would place eggs in front of them, and when they tried to go for the egg, or even showed the slightest bit of attention I would "disagree" with them by giving them a hardy "peck" ( poke with one or two fingers ). Aiming for the top of the head is what chickens will most often do to others, but you can also "peck" their backs or thighs. The idea is NOT to hurt them or send them reeling or anything like that, but rather to break their concentration and refocus it elsewhere. Make sure you have a treat on you, so that whenever they clearly IGNORE the egg, they get a treat.
It took me about a week or two to retain my girls. I have no problems today, and I still have the girls that were egg eaters about a year ago. I understand that taking the time out to train your chickens isn't in everyone's schedule, but I would highly advise that people start using training as an invaluable tool in chicken keeping since they are highly intelligent and social animals, capable of recognising over 150 individual faces and voices for up to three years, grieving the loss of flock mates, learning from observation ( even watching television ), and much, much more.
I train, rescue, rehabilitate, and rehome chickens as a hobby and occasionally for hire. If you are interested, you can check out my blog
[here] , and if you have any specific inquiries, feel free to Email me. I hope you manage to fix your flock problems!
I really don't want to have to kill half my flock, I really like these chickens. 
