Hi. I am an experienced herp keeper that has encountered the same problem that you have. I've tried everything, some things without success, and have found a few remedies that are like magic. First of all, to kill the mites on the snake itself, nothing works like good old fashion vegetable oil. The oil is thick and it sufficates all the mites in minutes flat. This is a bit messy, do it in a bath tub or large sink. As for the cage, the method of getting rid of mites really depends on what materials the cage is made out of. If the cage is plastic, water and a disinfectant cleaner will most likely work. If it is wood, it probably won't do anything.
The ULTIMATE mite killer is Black Knight Roach spray, it is what they used years ago to disinfect people traveling to other countries so they wouldn't spread disease by lice, ticks, and other bugs. They discontinued it at the airports because of some longterm problems that where assumed to be caused by the spray. However, this was a rare case, for the most part, it is very safe. The only drawback is the availability and price if you are able to find any! I bought mine over the internet at Pro Exotics (US). It's about $20.00 a can! Nothing works like it though.
My mite problem that was lingering on for months (just when I thought I got rid of them they came back!) Was gone within the first day, and hasn't come back. It is over a year since I've had to use it. Just read the directions on the slip that comes with the spray (if you buy it from pro exotics that is.) and you shouldn't have any problems.
Black knight can be used to rid the snake, the cage, the furnishings, the surroundings, and the room of mites!
One more thing, if you use the Oil idea to rid the snake of mites, dont' get the oil all over the snakes head!!
Good luck!