Have you tried DE (diatomaceous earth)? I love it and it kills the lice and mites. I use it on my chickens and rabbits and it's all natural. You just need to keep it from lungs and eyes. When the chickens aren't around I sprinkle it where the chickens take dirt baths. If I think one or more has a problem I will sprinkle it on their back with a salt shaker I purchased for just that reason. It has worked wonders for me.
Yes, I use DE, I put it in their dust baths and I sprinkle it in the main coop floor every week too. But I don't ever really see the Silkie's dust bath, I couldn't find any on my other birds, I looked for an hour last night, just on the Broody Silkie Momma that is sitting on eggs right now. so hmmm.....