I see. Sounds like you figured out the problem, then. At no time can there be sliding room. I had someone on BYC send me eggs in a similar way, but she had them packed each in bubblewrap, differently than your picture, though, then a number in each small rectangular box, each box in the large bubblewrap, then peanuts and newspaper, I think. Anyway, the key was NO SLIDING ROOM. Every egg must be snug. Also, the eggs must have good shell quality; no thin shells.
There are several ways that work, but they just can't move in the box. I also line the box with the large bubblewrap and styrofoam sheets, if I have them. So far, so good.
Sorry that happened to you! What a mess to work through!