I had the same problem in March, my local feed supplier suggested a higher protein feed. I've been using 19% protein feed since and the problem is mostly gone. I still on chicken that will still eat an egg, maybe every 3 or 4 weeks. The mustard did not work for me either, they seem to enjoy it.
I've tried golf balls, they don't seem bother with them. Maybe because they're white, my chicken lay brown eggs. With Easter around the corner, I'm hoping to find some brown plastic eggs.
I've tried the mustard trick on my egg eating chicken, they seem to love it. It's gone within an hour or so from me putting it in the box. I've tried the regular mustard and Dijon mustard. They love both.
I was thinking of getting a bunch of plastic eggs and see if that would confuse them...
I sure that chicken will eat dead mice, rodents, etc. If they found a poisoned dead rodent, and ate it or even some of it. They could have taken in the poison. If I use any poison, I make sure there are no dead rodents laying around before I let the chickens out.