Could you split a hive that you like the genetics of like a false swarm? Take the old queen and some bees and put them in a nuc, and then leave the original hive with the majority of eggs and brood hoping they will make a new queen?
The reason I ask is because of the previous postings along with the fact that I finished my round of inspections today and even though I have to go over my notes and records to confirm this, I think 7 out of the 8 queens I bought this spring are toast.
I know this really falls under another category, but it seems like we're on a really nice role here!
Of course you can do a split as you suggest. In that case, I would move the old queen, 3 frames of brood, and two frames of honey/pollen into a new hive box. You could use a standard 10 frame box and just start a new hive. The old hive will have all the foragers and will, with any luck, raise a new queen. But that way you only get one new queen. You would also want to check that there are still drones flying where you are.
If you are wanting to replace 7 queens, you will need to take some of the queen cells produced in the old hive that has good genes and spread them around to hives where you squish the queens. I would squish the queen in each hive and then add the queen cell within one day. That way, the hive won't kill the new queen cell and the queen cell you add will have a head start on any of the eggs in the hive.
But it's late in the year to do any of this unless you have a strong fall flow and are willing to feed sugar,