Rub mineral oil on eggs and that will act as a preserver.
Here’s how to make a zeer refrigerator that is a small pot inside a large pot with sand in between = http://www.wikihow.com/Make-a-Pot-in-a-Pot-Refrigerator
I can’t find the link but there is a refrigerator made from basically a box with a cloth or burlap draped over. Make sure it stays damp and that cools the food. From Australia, iirc.
I wished the heck I’d known the mineral oil trick. Aldi had large eggs on sale for .69 cents per dozen.
(disclaimer - I’ve eaten eggs 30+ days beyond the printed expiration - they tasted fine!)
Old camping technique.
We learned to make them in the Boy Scouts out of orange crates and burlap bags.
They work on the same principle as the "swamp cooler" type air conditioners.
Keep the burlap wet and the evaporation keeps the contents cool.
Something like this:
Just Google "evaoporative cooler" to get some ideas.