Well this isnt a sure fire way but when I had a break out in my mice tanks a little while ago while I was cleaning the cages I used some strong bleach water in a spray bottle. They seemed to die right away. Of course that doesnt help you with the animals but it could keep the mite population down until the stuff arives. Maybe you should go with the nix and soak the dishes and spray the surrounding area with bleach. Ive also heard that the bleach will eat the outer lining to the eggs and kill them as well.
If youre happy and ya know it slap your face!