So i had the house to myself overnight for the first time in over 20 years a few years ago and got to watch a ton of bee videos with out anyone complaining. One was from the university of florida about varroa mites. It said that the mites are triggered to go in the cells by a pheremone the bees emit to cue the capping of the cell. They enter just before the cells are capped.
What if you took a frame, removed the foundation, replaced it with a sticky board. Now cover that frame with #8 mesh so mites will have access to the sticky board but the bees would not. Then spray a synthetic capping pheremone on the stcky board. Place this frame in the brood area and it should attract and catch mites without harming bees or honey. Just need someone to isolate and reproduce the capping pheremone. Would be easy to use multiple times or even continuously. Bees might try to "cap" the mesh or maybe not since the #8 is completely different in size and shape to a cell.? Not sure, might have to clean hardware cloth with a torch periodically. If they didn't gum up the hardware cloth maybe you could just use a stcky board under a screened bottom board?