Being new to all of this still I once again rushed out to be by her side when I heard the characteristic call, which you can hear in these little videos. I opened the servants' entrance to the coop and had a good view of the closer nesting box, where she was sitting.
Her sisters were there for moral support, which I thought was very kind given the recent kerfuffles they've been having. She was quiet for a while and nothing seemed to be happening, so I went back inside.
A few minutes later I heard the call again and went out to check, and sure enough, she had done it again! I made sure to tell her how proud we were, and she seemed pretty excited about it too.
Looks like we won't have to divide that first special egg in too many parts after all. Life is good here on the farm.