How often do you gather the eggs? Do you have to gather everyday or can you gather every three days? If you gather every three days are the eggs still edible? Do you need to clean them with special stuff? Do the hens care if you take their eggs?
So many questions! I was in your shoes last year. I would collect eggs daily, in the summer 2x day if possible. I would never leave them for 3 days. I never clean them unless really dirtly. I clean them with a warm wet cloth and just wioe them before I give them to my customers and before I cook with them. My hens never mind, the delawares always expect something in return so while I'm handing out treats or while they are eating I take their eggs. They are usually very proud of me taking their eggs as if to say"look what we did for ya mom!"
I get the eggs every evening, wipe off any loose trash from them and wipe the ones with stuck trash with a wet paper towel. Then I cartian and refridgerate. Some hens mind and some don't. If they mind I quickly remove the hen from the nest so I don't get picked. Unless there is a broody or one wants to roost in the nest, they are usually all off the nest by evening.
Some people keep there fresh eggs at room temperature for a week at a time, saying there best if not refrigerated. The best for hard boiling are month old refrigerated eggs. So you can see eggs can last. I gather once a day and have been know to skip a day by accident.
Leaving them for three days increases your chances of them eating their eggs so it's not encouraged. Once you have an egg eater on you hands their hard to retrain.....