tbone3636,
I've been working on this very same problem, though your task is a bit more daunting. I have only 6 laying birds and two birds that should be mature enough to lay towards the end of summer. Egg to bird indentification may be done if one can track individual chickens and then match them to a known egg type. This could be estimated in a statistical sense to see how well one can classify an egg to a bird (see discriminate function analysis). However, I'm pretty certain that the variation among eggs for an individual bird is just as large as the variation among eggs for all birds - so my hope for this is limited.
Another way I thought of was to use a motion activated go-pro or gamewatch camera so that I could monitor snap shots of which birds enter the egg boxes on a daily basis...
As far as factors that affect egg laying check out my earlier post that quantifies how day length (day light), temperature, and bird age affect the probability of egg laying - its my post on climate change and egg laying.
I'll let you know how well my egg identification goes, though its labor intesive and preliminary data suggests its not going to work. The motion sensitive camera to identify individual birds may be the best option...
Cheers,
Fish Chicken