The dish soap in the water for a soak isn't to eradicate the problem, its to give the animal some immediate relief. The dish soap breaks the surface tension of the water. When the mites get caught in the water they can't float anymore so they drown and die.
Use the PAM every 10 days for a month, you should be just fine. If the snake will stand being soaked you can do that to, but use regular water for the first few minutes because they'll drink it.
I pre-treat all new arrivals as well to make sure I keep mites out of the rest of my collection.
I had a honduran milk snake that I got from a reptile shop a few years ago and she had the WORST mite problem I'd ever seen. They were pushing up her scales on her chin and crowding around her eyes. There had to be at least 30 of them that I could see. The PAM did the trick, I just gave her a soak to get some of the mites off of her.