This may not help you but this is what I do:
I keep two 18 count egg crates in my inside frig. I fill up the front one first as I collect eggs. Then I fill up the back one. We use from the front one first and every couple of days I move all the eggs forward so that new eggs are placed in back.
If I have two many eggs for those two cartons I keep another 18 count one in the garage fridge and put the very freshest eggs out there. Does all that make sense?
For boiled eggs I would put a dozen or 18 in a separate carton and put it to the back of the frig for a week before boiling. Mark the carton for boiled eggs so nobody uses them for anything else.