I build this design for all my hives. I've even used these plans for my Warres. This is the fast and clean method.http://www.myoldtools.com/Bees/bottomboard/bottomboard.htm
You could router the bottom frame of your TTBH, 1/4", down both sides, and slip in two, two feet long bottom boards that meet in the middle. Then you could pull them out, or open them just a little for ventilation. Put your screen above the sliders. I don't really know how much good a screened bottom board does for mites, but for me, they work wonders for ventilation. I pull my sliders out about July first, and don't put them back in til about Sept. 15.