Wow, only real way to end it is to cull and that is not my desires! Possibly could you pick up some wooden eggs, paint them the colors of your birds eggs, placing a number of them, 4-6, then when they lay, possibly getting no response from the wood eggs, they will go from them.
Also changing the nest material, covering the one nest box that the egg eater goes in. Also, if you can find "glasses" for the girls that are doing this, then it often breaks them of feather picking...perhaps egg eating.
Good luck and hope you get a better answer then myself.
ps- I wonder if you hang lettuce of something just out of easy eating reach, that they would be more eager to work at that then eat the egg they just laid, also increase protein and it may help.