I have had success with the specially designed plastic egg carriers made for camping.  They still must be handled carefully and watched that nothing gets set on the egg container.  IMO you need to put smaller eggs (medium to small) into those plastic containers.  The large and extra large size grocery store eggs are too big for most of the manufactured containers for camping.  I put the carrier into at least one, sometimes two, zip locks to make sure no leakage occurs into the rest of the food pack.  I use any eggs that get cracked, first.  I usually only take a dozen or less fresh eggs, and also take dry egg powder for cooking with and backpacker style freeze dried egg dishes for egg meals after the first week of being out camping.   8-)