Old timer here. I only know of one "natural", "herbal", etc. remedy for mites in nest boxes, and it's likely not something you can get at this time of year, nor am I sure you will want to use it. That is tobacco stems. As an old time pigeon fancier, I can tell you we used to put tobacco stem bits in the nests. Depending on where you lived, you could get them from a farmer who raised tobacco, or some people grew their own. This isn't the ornamental tobacco grown for it's scented flowers, but the kind used for pipe or cigarette tobacco; I don't know if the ornamental kind would work, although since it's poisonous too, it might.
The thing is, remembering back to when I worked part time in a greenhouse, nicotine from tobacco was the most poisonous, most dangerous stuff we ever used as a pesticide. I don't know how toxic the stems are to a bird nesting with them. I can tell you that it had no ill effect on the squabs, and it did keep them from being eaten alive by red mites in the nest. I'm assuming this is the same kind of mite thats a problem for purple martins, because they are found in the nests of a lot of "wild" birds like starlings, they suck blood, and a heavy infestation can kill the young in the nest. You don['t see those much any more in our coops etc. What you sometimes see on pastured chickens (from exposure to wild birds) is Northern Fowl Mite, which is bigger and runs around under the feathers. It's an irritant but not life threatening like the red mites, and easy to control by dusting with the poultry/livestock pyrethrin powder as suggested earlier.
All the rest of the herbs you can grow around here that I know of are just aromatic, and may deter some kind of bugs from moving in, but don't kill them. Outside of herbs you can grow locally, of course, is the pyrethrum chrysanthemum where pyrethrin comes from; those flowers are also an effective insecticide but they are use by grinding them up, and not healthy to breathe the dust all the time. Hope this helps!