Organic grower here too, in the garden, lawn and fruit trees. Sometimes, though, "natural" methods are ineffective and worse put focus organisms at risk because of their lack of effectiveness. I think a person should use the safest product that actually works, and natural products are not always even the safest option.
Provent A Mite is really, really safe when used according to label directions. Pemethrin (the active ingredient) is very stable on surfaces once it has dried, and only the bugs that crawl on it get exposed. It has good residual effect, so continues to kill mites that return. Dermal absorption in reptiles could be expected to be very low (it is low in humans, and we don't have scales). It is safe enough that it is impregnated into human clothing for tick and other insect prevention, and even used in shampoo for lice elimination.
It is pretty dangerous to amphibians, though (since they absorb it through their skin), so either remove the frog from the room or take the snake's enclosure out of the room to spray it and don't bring it back into the room until the PAM has dried.
Organophosphates such as the dichlorvos in No Pest Strips have a far worse safety profile, and are "a major cause of animal poisoning".
Mites are a serious health problem and should be addressed very aggressively, in my opinion. Maybe not so critical if there are no other snakes in the collection, though they might be a disease vector to wild snakes in certain situations.