I know the one hen that lays regularly and and the biggest eggs for me occasionally eats the eggs. I'd been thinking she was pecking at the ends of all of her eggs too, but recently realized the bedding in the nest got too thin and the eggs were breaking when they landed. I know cjeanean said she had a roll-away nest box plan--something I plan to do with my nest as soon as I can squeeze in time. lol It's really infrequent that she eats the eggs, and there is always a bit of shell left over (as far as I can tell, anyway). I would try the roll-away nest boxes if the bad-tasting eggs don't work for you.
Good luck!