Eggs layed in the feeder

I have a galvanized feeder hanging in the coup. The feeder is one of the 3 gallon things, much like the galvanized waterer.
It hangs very close to the roost and to a ladder leading to the roost. It doesn't hang by design it just happened that way.
For the last few days I have discovered an egg, sometimes two inside the feeder. I assumed that one of the hens was hanging her backside either off the roost or the ladder to allow the eggs to drop inside. I have been keeping the feeder half full to make for a softer landing for the egg.
Today, I picked up all the other eggs, then checked the feeder. This time I found a hen inside of it. She made no attempt to get out despite some encouragement from me. She isn't the biggest hen I have, but it is still a tight fit for her inside the feeder. After a minute or so I picked her up and placed her in a nest box - trying to make a point to her. She didn't think much of my plan and promptly left the nest.
A couple hours later I checked on them one more time before leaving. Naturally, I looked inside of the feeder. This time there was another egg and no hen.
This particular hen is the most mischievous of the bunch. She will fly up and land on my shoulder without invitation. When it is snack time, she'll try to steal the goodies from the bigger hens and get mugged for doing so - but she keeps on doing it. She also complains the most if she feels she isn't getting her fair share of goodies.
I guess I have to put a lid on the feeder now, just because of her. She is nothing but trouble