So, another question: what's the purpose of the QE in the Demaree board?
The Demarree board is just a tweak of the original Demarre, there is no
need for a board at all, or for that matter an upper entrance. So firstly you could just go with just putting the top box on with no QX and no upper entrance
The upper entrance serves just one purpose - allowing any drones that have emerged in the top box to escape
Some people get their undercrackers in a knot about drones getting into the supers, this is a non issue unless you are foolish enough to use porter escapes for clearing, but a QX stops the drones getting into the supers.
I use Demarree for both swarm avoidance and making increase. Often, especially with a strong queen, the amount of pheromone getting into the top box is strong enough to supress the urge to make supersedure cells, by using a solid board (with or without an entrance) with a small aperture in the middle (with or without QX) reduces the amount of pheromone getting into the top box thus aids QC production.
You could put a piece of mesh over the hole but then that would mean the two boxes would function as two separate 'colonies' and make reducing the hive in the autumn a bigger challenge.
Putting a piece of QX over the hole serves to stop drones getting in to the supers (not really a big deal and serves no logical purpose if you then put shallows over the topmost box)
Using a QX also stops any new queens which you inadvertently left developo in the top box from getting down and laying in the shallows.
free movement of bees between top and bottom boxes is important. Everything else is just tinsel.
