Just to add my two cents in here. I shipped some eggs using the big air bubbles (3 x 4 inches) with newspaper, and had one break enroute. Won't do that again. I', thinking one of the bubbles must have gone flat.
I just received some special eggs from a wonderful lady willing to share. She does not normally ship eggs but did an incredible job of making sure they were safe. She used plastic - not foam egg cartons, put shavings in each one, then the eggs, then filled up with shavings and closed. She wrapped the cartons in several layers of small bubble wrap, taped, put in box with newspaper all around and shavings, then filled the entire box to capacity with shavings. There is no way those eggs moved within the box. Two dozen eggs made it just as snug as a bug. Yeah, it was messy and had to be opened outside, but I think I will start packing that way.