Geeze, Buttons, I would have guessed you had been through this a million times by now given your spectacular collection. You may want to consider the following actions. YOU are the one on-site and closest to the plants and are therefore in the best position to determine what to do, and what resources you have available to do it. With that caveat here are my recommendations:
Step 1: Eradicate all spider mites, mechanically, then, if necessary, chemically. You can use an old soft tooth brush and cool running water if the cactus flesh is sturdy enough to handle a light brushing. Use the mildest mitocide available to you in your country - or your organic insecticide of choice. See for ex:
http://www.liquidladybug.com/?gclid=CKKRhdSszbkCFVGe4AodKD8APwMultiple treatments will be required as the eggs will (may) not be killed by the pesticide. Typically, reapplication will need to be done every week or so depending on temperatures. At higher temperatures, the mites reproduce faster and more frequent treatment will be necessary. Since most pesticides will create a phototoxic reaction on the cactus epidermis, it is best to keep your plants out of direct sunlight after treatment for several weeks.
Step 2: IF NECESSARY, do as PermieGing said. Use a scalpel with a # 10 blade or sharp single edge razor blade and cut the cactus just above the border of the tap root by 2 - 3 mm. Plant the root stock and hope for the best. Wait 1 week to allow callus formation on the head, then set it on some moist, sterile sand.
S.L.