The bees are continuing to be confusing. Today I really got into the hive and found a couple of things. (1) They still haven't started drawing comb on the flow frames, so I rubbed beeswax all over them in the hopes of enticing them to start. (2) There were more queen cells, including a few emergency queen cells. (3) Close inspection of every single frame showed me there were no larvae anywhere. Which means there is a problem with the queen.
So I left the queen cells I found, and closed it all up again, and emailed my bee mentor. Hopefully he has some ideas. They definitely haven't swarmed, and they definitely have room in there, so fingers crossed this is the right decision.