Exactly. One day wouldn't necessarily catch all the layers, but it will let you know if you're getting eggs or not.
You'd be amazed at the places they'll hide their eggs.
I think I may have a solution.........
You stated your birds free range. I'll bet you have hidden nests all over the place! Go on a serious egg hunt, and I mean look everywhere. Under bushes, behind garbage cans, I mean everywhere. Remember, as far as they know the survival of the species...