On my first couple of trips ( a long time ago) we solved this issue by bringing a live chicken with us. Fresh eggs every morning!

The downside was the hen waking us up early every morning. Like crack of dawn early.

She was good in the canoe and even learned to wet-foot all the landings.

Alas, we lost her on Have A Smoke Portage...some disagreement in our camp if she just wandered off or was a tasty meal for an opportunistic brush wolf.

The Beaver

On Spring and Fall trips, I have cracked a dozen or more eggs into a Nalgene bottle before hitting the trail. Once I reach camp, I place the eggs and other refrigerated items (like cheese) in a mesh bag and sink it down a ways in the lake. Nothing beats real eggs for the first mornings breakfast.

As far as egg carriers go—I often take a few fresh eggs to use in baking or some special meal. I save used cardboard mailing tubes including the plastic cap ends. Place a bit of paper towel wadding in the tube, slide in an egg, another wad of toweling, another egg etc., etc. You need to coordinate the size of your mailing tube to the eggs you are transporting of course so you don't get excess rattling around. The tubes are easily cut to length with a sharp knife or a bandsaw if you have one in the workshop. When the eggs are used up, burn the tube and bring the plastic caps home for the next trip.

Canoefly