The 6th grade is having an egg-dropping contest today. They had to design a container that would keep an egg from breaking inside it. DH and DS went low-tech with a cardboard box, a bunch of foam cut to fit an egg perfectly inside it, a baggie for the egg in case it breaks, and some tape. I hope it goes well, DS was pretty excited. We did a test drop from our second-floor landing to the kitchen floor below and the egg was still in dandy shape, but it was one of "our" eggs and so the shells are a lot harder than the store-bought variety they'll be using. I wanted to send an egg but that wasn't allowed since they could be hard boiled.
You and yours have the upper hand having eggs made for you daily and knowing well enough what will most likely work best since I'm sure you've read plenty here on how to package eggs for shipping/hatching.... so on that note...ha ha...I hope your son is the winner.