Another option to kill the mites on the spot is Adams Flea & Tick spray for dogs. Make sure it is the one to spray directly on dogs, there is also a Home version to use on upholstry and linens.
My oldest DD helps do the vet check at fair every year and this is what they use if they find a minor case of mites. Bird gets sprayed down and put in quaranteen and gets rechecked later at the end of the day. If they are as bad as you say, I would spray the bird down under the wings, around the neck feathers, near the base of the tail and around the vent (not ON the vent). This will kill all the mites that get wet from it. I would follow up with the Seven in the coop and dust the bird when it is dry from the spray. You may need to repeat this process every few days until you see no signs of mites. And remember to treat ALL the birds that are in that coop! If one has them, the rest will get them if they haven't already.
Good luck!