Not respraying with acid, right?
Also, you need to treat your birds every week for 3 weeks or so to kill the adult mites and then the eggs and any critters that hatch. And, you need to clean the coop and treat each week that you dust your birds as well. If you don't so these things, the mites will most likely come back. I've used Sevin dust, there's also Garden and Poultry Dust with Permethrin, Ivermectin, Poultry Protector...all of which need to be used carefully, especially around their heads. You can cut the toe end of a pair of panty hose and fill it with the powder, tie it and use it to poof them, getting down into their feathers. Dawn might work, but too much peppermint oil would be irritating and probably even painful from my experience with getting peppermint oil on my skin. Neem could work, but I don't know how you apply it. With all due respect to shortgrass, I do not use DE or wood ash, both of which I believe to be harmful to their respiratory tracts. Many people use these things, and many do not. A dust bath is important though. If they are in a run, make sure they have a good area for that.
Search the BYC site and you'll find more information. The Chicken Chick shared a link with the U. of Mississippi that provides a list of pesticides you can use, other areas of the site discuss these parasites -
http://msucares.com/poultry/diseases/pesticides.html
Whatever you use, use as directed and don't over do it! That may eradicate the mites, but could harm your birds. More is not better! Use just enough to accomplish the task. Mites are awful, but you have to approach this with appropriate products and be absolutely thorough about cleaning and re-dusting. Also, as an aside, I'd give my birds some vitamins and maybe some extra nutrient packed treats to fortify them through this. If they are infested, and if they have been for a while, they could be a bit anemic. You'll want to check them over to be sure their skin is in good shape too, as the mites can cause pretty serious irritation (another reason to be very careful with product application, especially peppermint).
I'd plan this out a bit and then launch the attack. Good luck and let us know how you do.