Long term egg storage used for "Centuries"
There is a long term answer to egg storage used by east Asian societies for centuries. The product it produces is called a "century" or "thousand year" egg.
I have not looked this up online but discovered reference to it in a Chinese cook book maybe 10 years ago. The process, if I recall correctly involves a hole in the ground, clay pots, straw, and a horse with a penchant for urinating in said hole.
Eggs are then "pickled" in situ, kind of like Kim chi. The result and I say this from experience, will set you free.
I procured some "century" eggs from a local Asian store here in Chicago a couple years back to offer up as a New years delicacy to family members. All except one flatly rejected the idea. The only taker was my brother in law who I offer up little "tastes" in the annual "bet you wont eat this" New years challenge.
Result: He ate it but said he would never do it again.
I was unable to finish even one.
Picture Gray shell, dark amber white and dark gray yoke. Texture was similar to regular hard boiled egg. Taste on the other hand had nothing to do with eggs, or food, or really anything that should be handled without a has mat suit.
My opinion. Dont do it.
I buy dried eggs in a can. They could charge 10x's as much and I would still call it preferable.