What if you put that EE hen in a cage overnight, get her egg before they do, and shoot a bunch of food coloring into it. Put it back in the run and then whoever eats it will get their mouth dyed bright blue or whatever color you use. I busted some by just putting an egg in thier feed dish and two biddies dove for it like it was the winning lotto ticket or something. I snatched them both up and took them right down the road to a chicken trader and gave them to her, with full disclosure.