We have a queen!
My little split here, which we started on April 23, 2022 has successfully made itself a queen. We checked it on May 19, 2022, and there she was, doing her queen stuff. They don't need a second box yet, but probably when she gets busy laying eggs, it will happen quickly, so I will look for increased activity on the entrance, then check when I see that.
Also on May 19, 2022, we checked the other two hives, which are going gangbusters. The blue long hive has so many bees it is incredible. They also have at least five or six full frames of honey - deep frames - behind the brood nest. We removed two frames of brood from that hive to help make up a new nuc. We checked the tan hive, and its bees are a little testier. I am not sure if it is the bees, or the fact that they have had to fight since they were installed against robbers. We removed one frame of young brood and notched several cells for a nuc.
We put the three brood frames in a nuc box with the notched frame in the center. I added a couple of frames to it, one with drawn comb, one with honey and a third that was empty foundation. That nuc went off to its new home later in the day. I will follow up to see if it successfully makes a queen as well.