Which is me, as I raise my own queens. And I'm in the centre of Boston. But I'm a game beekeeper who does flood the area with own drones to ensure good mating in both apiaries.
Another question that I have is as the OP has the queens in mating hives whats the plan once the original queens have been squished?
My own plan would be to install new queens in spare hives. At night time move the original hives to new spot. Put new hives with new queens in the original hive positions. Next morning, flying bees will leave old hives and return to new ones headed by the buckfast queens. That will reduce the number of bees in the old hives making it easier to find queenie.
Further to this, to increase the new colonies quicker. Open the old hives and shake the bees off the frames and give the ones with capped brood to the new ones. The old colony will have less brood frames and therefore less frames for queen to be found on. Should be able to find her on these frames now.
Once squished, unite the two colonies using the newspaper method.
I'd come and help but I'm majorly time constrained this week and next, and you need to find a solution quick to ensure they don't buzz off when the mating hives are full.
baggy