> There are ways to render colonies broodless and keep queens laying. 

True,  and in broodless clusters all kites are phoretic, making it easier to get an almost complete mite kill, but broodlessness is usually an abnormal and often undesirable condition.  (Exceptions noted).

With that in mind, it is useful to bear in mind that in a normal colony with brood most of the phoretic varroa are to be found within inches of open brood.  If a queen is laying and brood hatching and being capped, if there are varroa anywhere in the hive,  most varroa will be there. 

When doing alcohol washes, a sample taken ten inches away from open brood may reveal as little as 10% of the number found in a similar sample taken in the same hive at the same time but from bees on open brood. (Actual documented experience).

The open brood area is the target zone for mite treatments. 

In broodless hives,  I assume the mites will be distributed  somewhat evenly throughout.  The broodless state allows the mites to die of natural causes or for mite-chewing bees to access them, but while still on comb, some of the treatments possible on combless swarms is not permissible or advisable so broodlessness only interrupts the mite reproduction similarly to the interruption in bee development, so seems to me to be a weak control.

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