They will also change the spots they are laying when you find a nest and remove the eggs (depending on the hen). I have a stubborn hen that will make a nest, I'll find it, and she will made a nest some place else. Everyday I get to go on an Easter Egg Hunt!
You probably already know this but I...
My hens usually dig a small crater like hole in the past they make a nest at the base of perennials, in tall grass, one even had leaves nearby and pushed some leaves to cover the eggs.
There are feeds that help with molting called "Feather Fixer" but this isn't organic. I haven't looking into...