Hey there Fairbanksian!
I had an egg eater, she became dinner. It's next to impossible to break them from doing it. Now I won't dispatch any that eat the broken egg, that is normal for them but if I catch one actually pecking the egg to get into it, she's becoming a meal. If you egg breaks during laying, put some straw in there to cushion the egg when laid. I've had a few break when we have 16 boxes and every bird has to use box #2, by about the 5th or 6th egg, one will break. Just have to go out three or four times a day to collect them, prevents the breaking from hitting another egg.
Good luck up there, we've been -20 here and my birds are not happy about it.