I wonder if your permethrin is old and has lost potency. If we mix ours in the plastic sprayer and leave it for more than a week or so, it looses potency. And the Gordon's concentrate changes color over time, and has an expiration date.
Spinosad will work, is expensive, and as everyone has mentioned, whatever you do, the coop has to be emptied and treated too.
Here we have wild house wrens invading the coop daily, and they bring mites inside with them. It's a royal pain!
In the USA, and many other places, Ivermectin is not approved for use on chickens, which makes the official egg withdrawal time forever. It works very well for a lot of parasites, and is easy to use, and many people who do use it throw eggs away for varying numbers of days, anything from one to four week is typical.
Nothing will work if the bedding issue isn't dealt with.
Mary