We have had some egg eating occur here, but not quite to the extent you describe. When It happens, each nest box gets fake eggs, and the favorite box gets many fake eggs. The more eggs they peck and don't break, the better! We bought wood eggs this last time...actually had ceramic ones break, and the wood ones are not quite the exact shade of real eggs, so easier to disregard when collecting real eggs. In fact, the ceramic ones look so real we had to use paint markers to write “fake” on the eggs, and a few designs so we could distinguish them.
the chickens really love eggs...one day collected one egg and was standing in The run (egg in hand) talking to my kid. I wasn’t paying attention to the chickens and my hand was by my side. All of a sudden a chicken jumped up and pecked the egg (and got my hand a bit) causing me to startle and drop the egg, which promptly broke. The chickens converged on it. But, other days we sometimes find an egg that was laid in the run...untouched, not pecked or broken, just waiting to be collected.
nice coop! Very attractive. Good luck with getting the egg eating stopped.