Sounds like things are under control. And based on my knowledge of mites, though not hands on, I would basically treat as if you've got a full blown outbreak. These mites can be pretty good at hiding out somewhere and hitching a ride when the time is right. Treat any fabric surfaces like couches, carpets and beds the snake was in contact with. Change and wash clothes any time you're treating, handling, etc...
My understanding is better safe than sorry and overkill is a good thing when treating for mites.
As for the dish soap thing, just soaking in plain warm water will drown the mites, no need for the soap.
If I'm wrong in any way, hopefully somebody more experienced will correct me. Good luck and keep us posted.