I would agree with Michael Bush. If you are wanting to change the genetics of the mites, then you could either eliminate all mites which select for drones, or you could encourage mites to select drones. From what I've read, one wants lots of drones! They collect mites, and if you have a good hive, they spread that good genetics. And seems like I recall reading they serve some additional expendable purposes.
The bees want so many drones for the year. If you are killing them, they will keep on trying and trying. Let them get it out of their system. Mites naturally prefer drones. If you could encourage them to be totally dependent upon drones, then so what if you have mites in your hives. Might not quite happen that way, but what about the alternative. What if you were to select for mites which only selected workers?