Greetings
        I hate to be the doubting Thomas but I personally don't see
how the screened bottom board could work. I have watched mites cling
tenaciously to bees and find it hard to imagine very many simple fall
off and can't get back up. The mites that do fall off may simply be
mites that are old and no longer strong enough to cling.
        Think of a hive full of bees and frames, and possibly a
certain amount of burr comb, and  think of a mite losing its grip. Is
it going to go tumbling all the way to the bottom like Alice falling
down the rabbit hole? Or simply drop a few centimeters onto another
bee, or get snagged on a piece of comb?

PB