Im sorry I wasnt clear. I would like to retrieve eggs that dont need to be cleaned too much.. I tried a slanted astroturf bottom and the eggs rolled to the back but with 12 hens, they still manage to lay on them and they get dirty!
It seems like your nest box is ideal for keeping the eggs clean, so I'm wondering if the problem lies elsewhere. Is there a lot of mud where they spend most of their time? What do you use for bedding in the coop? Do you have some hens who like to sleep in the nest boxes rather than on the roost? Do you have chickens with feathers on their feet? Are their backsides dirty?
ETA: Are all 12 hens sharing one box, or do you have more than one nest box?