Happily, I've never attempted to live on the wartime ration.
But I want to offer my favorite way to prepare for the occasional lack of eggs, as Nancy points out,
I think for me the forwards planning would be tricky - I tend to look in the fridge and say - what shall I have tonight? Partly because I don't know what I will have left over in the shop. But one egg?!
Keeping a stash of flax seed in the fridge, I have yet to find an application where the "flax egg" as an egg substitute doesn't deliver a quick victory over a limited ration. For each required egg in a recipe, substitute 1 T flax seed (ground to flax meal) and 2.5 T water. I've used this in everything from meatloaf to waffles and the flax egg works perfectly every time.