Just to conclude this saga, I had another small swarm which I put on top of this hive, trying again to provide them with a queen faster than they can make one. Yesterday I checked and the virgin in the top is now laying, which is great. Then I checked the bottom and there was BIAS and not a single queen cell!
So I guess there was a mated queen in there after all and I somehow just missed her?! Who knows. Now I've got two queens instead of none.
I figure I'll just keep the one in the top as a spare until swarm season is over. If I don't end up needing her, maybe I'll put her in her own hive, or just use her colony as a support hive.
Thanks for all the help throughout this whole thing, everyone. Never a dull moment!