Northern Fowl mite lives on the bird so it is not necessary to clean and treat the coop itself
Not certain what essential oil mix you used but I doubt that it will kill your mites. If it does you will still need to follow the 5-7 re-treat cycle recommended by
@Wyorp Rock above as their eggs will hatch and re-infest your birds in short order
Permethrin is the most commonly used treatment and is VERY effective. Costs about $10 at TSC for the concentrate and will last you years so well worth the money.