Thanks again to all those great replies to my original two questions!
Today, I verified that the hive IS queenless (and still cram-packed with bees!), then I checkerboarded the three full sized brood chamber boxes to the best of my ability. The two upper boxes are now configured approximately FFPBBBPFF and the bottom box is mostly full of old honey. I had NO brood or eggs, so the brood comb is mostly empty. I hope that's a satisfactory configuration for the hive. If not, please advise what I need to change.
I have a new queen (in cage) which I want to introduce tomorrow after the bees have settled down from todays re-arrangement. NOW MY QUESTION: Where (which hive box of the three) should I place the queen cage?
Since it's the middle of the honey flow here, I plan to add a cut comb super after the queen is laying.