Maybe I'm missing something here but is there really that much of a "problem".

(1) De-queen as many hives as you need to meet your drone needs.  Queens can be "nuc'ed" for reuse later.

(2) Prevent new emergency queen from mating.  Either introduce a clipped virgin or use excluder(s) to prevent flight by an emergency virgin.  You can CO 2 the virgin to speed up start of laying.

(3) Once you have enough drones, either re-queen or re-introduce the original queen(s).

Anyone who knows the least about queen rearing can add all sorts of "go fasters" to enhance drone production, i.e. syrup, pollen patties, etc.  Other than maybe some messed up brood comb no long term damage.  Timing and co-ordination are the major issue.

Rip

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