Peter
The screened Bottom boards are not for the purpose of eliminating V Mites.
Their function is  the ventilation feature as well as keeping debris
normally accumulating off the bottom board. The board  ( Can be  Cardboard)
beneath the screen serves the purpos of monitoring the mite " drop off".
The side effect of the SBB is a reduction of mite propagation because the
fallen mites do  / cannot return to the bees. The mite population increases
with the seasons time element , causing eventual demise of the colony.
Quality  of stock or breed does not seem to enter the equation.
I keep adequate control with the application method of FGMO and have not
lost a colony to either V or T mites.Of course It is up to the individual
to be the judge of her or his method of treatment.
Best regards
JDF