Have you noticed the snake soaking at all? That would be a tell take sign of mites, especially considering you've already seen one.

...and I definitely wouldn't soak my snake in dish soap.

Sounds like you took all the right steps with the enclosure, now just treat with a proper product.

I've got no experience with mites, but I believe the treatment needs to be thorough and only certain products kill the eggs if any are present.

I'm sure somebody with experience with mites and knowledge of the treatment process will be along as the morning progresses.