Sounds like a good plan. Check for eggs several times a day, as much as you can, and hopefully that will narrow down if they are actually being laid in that condition or not.
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You may have a broody hen who is moving all of the eggs to a spot where she can sit on them. Good to hear younfound the problem. I had a little bantam who squeezed under a nest box in a hollow area, and laid about 16 eggs once several years ago.
She had a broody who decided she was going to raise a family no matter what. She managed to hide 14 eggs. When they hatched, they were all roos. Every. Last. One.