After I wrote "Update on the Mess" I went outside to see how the bees were doing, and, guess what, they were swarming.
They swarmed into an elm in the alley behind our house. I pulled off the super, put it on a sheet of cardboard, caught the swarm, and dumped it in.
It looks like I'll be building a fourth hive tonight. I hope that this signals the end of swarm season for me. I'm out of room in my yard.