Ditto what Brushwood said about the mites' inability to climb back up...they're too small and the distance too great, plus I'm not sure if their sense of direction is that great, either.
Treating the ground is ok if you need it and shouldn't hurt anything. If you actually *need* the ground treatment then you've already had one or more hives slimed by the beetles...the situation being kinda like "after the cows out of the barn". Things that will defend against them *before* they are a problem: strong hives (mentioned a lot, but truly are medicine for several ailments), in-hive beetles traps such as Beetle Jail Juniors, etc., oil tray traps on the bottom, fine screening over the inner cover holes, a finger or hive tool smashing them when you see them. For a hive that already has a strong population of beetles a guy came up with the idea of placing some screen mesh (I'd say #8, he says #6 I believe) across the top of a large container and putting an inch or two of soapy water in the container. Then go through the hive shaking and bumping each frame over the screen...bees will bounce off the screen and fly whereas beetles will hit the screen and mostly go through into the soapy water and die. Kinda time consuming but if the hive is being overrun..... ?
Cinnamon *may* help with the ants. Different people have different results. I smear it around on top of my inner cover...seems to help, but sometimes some stubborn, tough ants deal with it and come into a hive. What I've started doing is setting boric acid bait traps beneath the hives...that seems to have worked the best for ants.
What size screen are you using on your screened inner cover? I've found that wax moth can and will pass through #8 mesh.