I don't know if you still can , I imagine so, but when I was a kid, I remember seeing glass, porceline and chalk eggs, just for the purpose of getting hens to lay, and to replace eggs that you took from them, so they would continue to sit, and lay eggs. At least that was what I was told then....
Hmmm, I wonder if you took those big plastic Easter eggs, and put in a nest box, if that would encourage her to lay bigger eggs?
Wayne