How we package our eggs
for shipping
In winter months we line the box with foil backed styrofoam insulation, all
sides, bottom and lastly top as seen in photo 4
We fill the bottom with shredded paper or
bubble wrap for cushioning
A heat pack is placed behind a piece of cardboard.
The eggs are wrapped individually and placed
on the bottom filling
Heat pack is placed here
Box is filled with more shredded paper or bubblewrap
Styrofoam that we cut earlier is placed on top.
I don't think it really matters what you write on the outside
of the box unless it is insured
(USPS will not insure eggs).  

I've had them marked fragile all over and still got to me
smashed with egg oozing out the side.