Algodoo

Just a cushion, but a very well-made one. Hardly ever has more than one break on the outside of the egg, and nothing ever comes out.

Edit: works a little better and I made it lag less. Cushion is as simple as possible for rendering and I rebuilt the bucket out of boxes for fewer collisions. Also converted parts of the shell to boxes for the same reason. No shape-changes were made.

EDIT 2: A bit of a change in tactics here. Rather than crumpling to absorb energy, I made it squish and rebound. It's designed to keep the egg in the center and wrap around it as it goes down, distributing forces more evenly and reducing strain on the hinges in a couple of different ways.