Today when Big Rog and I were doing a good inspection of C3 (now H1 - hive 1) of Rogers, we found the queen in the upper super where she lived all summer long (as did the other hives I've had this year. It's strange and I might have to assume something reoccuring in the bee world - maybe (think it might be a cicada thing as crazy as that sounds) but hey, anything is possible why you have ruled out the probable!
Starting her up to can't hurt in my opinion. As the frames are drawn out she'll make her rounds and as cells become available (and when most are already brood or food filled) she'll make her way down stairs to get that box going too!
The bees in Roger's hive we wall to wall and elbow to elbow, I'm assuming we had 100,000 bees in that hive which I know is very close to swarming! Roger has got his self the makings for adding a third super (which I was able to find for him) for either a feeder or get some frames from his local Dadants place (which I had one nearby - but started trying to power wash, it wasn't buiding up pressure right and it was cutting holds in the super better than it was power washing) and let the hive build up and not out.
Note: cause I imagine Rog might read this, after he left, the air got out of the system and the powerwash was working like it should - but either way, your boxes will last those Virginia ladies for many years
All that said and back to the original post - it will be interesting if the new queen (caged) can indeed over power the older failing queen and force an inevitable killing off of the old queen and slowly turn the hive into her domain. Please let us stay informed, but I think it's a great experiment and worth trying especially if rounding up the old queen is hard to do and/or if yo just want to try a method tried and tested prior by experience keepers. Great post thanks.