We have a queen!
I checked the little split made a month ago, today. It had a nice pattern of capped brood, larva and eggs. I did not check farther for the queen, that was enough for me. They were covering about six frames, but since our next field day isn't until August 8th, I added an empty medium super of drawn comb for them to move into if they need it. They may decide to chimney, but at least they will have room to do it.