You go to a lot more trouble than I do. I KNOW the chickens eat the broken eggs some and then smear the rest around. I've seen one run over and GULP there went the small pullet soft shelled egg in one fell swoop. I was apalled.
I know they are not supposed to eat the eggs but as long as they are not breaking them open to eat them, I can't really stop it. After all, they dig in the compost pile all the time.
Today there was some broken eggs in the flower bed (we are having a contest to see who can find the most eggs NOT in the box, so far I'm winning at over 50 eggs in 4 days. Our chickens went on strike while we were gone) and the goober rooster was over there chortling like he'd found corn and worms. Of course they all came running for a taste. None really stuck around to gorge, so that was good.
On the same note, a really dumb chicken is just plopping them out while she's on the roost. Rather loosey goosey there! So plop! Out falls the egg into all the nighttime poo and sometimes it breaks. Then there's yolk all over the hen house as they step in it and track it around.
Mostly though, they don't eat the whole egg. They just give it a good peck to see what it may contain, then make a mess.
Lately its felt a lot like dealing with 30 toddlers.