use half inch soft foam on the interior surface of the box.. then a hammock like contraption to hold the egg, and rubber bands attached to that.
In fact. you can run to the store and get an egg container people use when backpacking.
Then cut out one egg container.. drill holes.. attach rubber bands to it... and figure out a way to mount it to the box. Make sure you have rubber bands attached to all 3 axis, to dampen the blow from all angles... then if it strikes the edge of the box.. the half inch foam should protect it.
