I ship eggs by packing them in wood shavings inside a paper egg carton, then putting a layer of crumpled newspaper on the bottom, placing the egg carton diagonal inside the box, and shoving crumpled newspaper into the cavities left over. I put enough in that the box barely closes, then tape it up. I ship either priority or overnight - lately, overnight because it's been so bleeping cold in my state that I want them to get OUT of my state fastest.
So far, I hadn't had any broken until the last time, and I shipped those from work instead of the post office, so the shipping area may have mishandled - but then I only lost two of each batch.