Let me say I won't carry real eggs. Mainly I just heat water, pour in pouch and eat.

This may not appeal to you, but I'll mention the possibility of soft-boiling real eggs, which only requires the heating of water and a fairly brief boiling time -- about 3 to 3.5 minutes. This approach is almost as simple as the boiling water poured into a bag method you mentioned, while being far cheaper than any freeze-dried eggs you could find. Clean-up is easy, too, if you eat the eggs right out of their shells with a spoon.

Egg shells should be packed out, but any dehydrated eggs you bring will have packaging, too.