Moving the wood enclosure outside is a good idea. Extreme heat and cold will kill not just mites but the eggs also.
If the .5% permethrin product is PAM then just use as directed. If it's a liquid that you're applying with a spray bottle then I'd dilute it 1 oz per quart of water, which will give the same concentration as the NIX/RID solution that is commonly used.
I wouldn't soak/bathe the snakes for several hours, 15-30 minutes in warm water with a mere drop of dish soap to break the surface tension and ensure the mites drown should do it.
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