Success! For five days in a row, one of my three chickens was pecking open an egg and eating about half of it. I took the last pecked-out egg and filled it with a mixture of mustard and hot chili powder, then paper mache'd it closed at the end and put it back in the box.
A mere five minutes later, I went to check on it, and found that somebody had already pecked at it and then smashed it flat! (Not sure if it was in anger or surprise.) The black chicken was acting suspiciously sulky for the rest of the day.
Today I collected three unruined eggs. Maybe I'm jumping the gun a bit, but I think this method succeeded. I'll repeat if it happens again.