I was thinking about storing eggs because I bought 3 dozen for Christmas baking and have decided not to bake, lest I eat too many sweets. Last year I put 6 dozen eggs in my root cellar in January, and still had fresh eggs in early May (when the root cellar began to warm up with the outside temps).
What I did to keep them fresh was to line the inside of the cartons with plastic wrap, and then coat each egg with lard, and add a layer pf plastic wrap over the top. The idea is to keep the eggs from drying out (as well as keeping them cold). Fresh eggs straight from the hens have a protective coating that does the same thing, but most folks wash the farm eggs they sell so they "look pretty" but they don't keep as long as they do if unwashed.
Did you know you can also freeze eggs? It's simple, and if you raise your own eggs, the frozen extras will come in handy when production slows down.
Crack eggs into a small container or freezer bags in the quantity needed for recipes, such as "X" number of whole eggs, or yolks only, or whites only. Be sure to label, including quantity!!
If you don't use them for baking, they make great scrambled eggs.