I know what you're going through. Though instead of animals, I used to grow crops in a small plant bed I have in the backyard - my tomatoes and apple tree were infested with spider mites and the symptoms were there.
I have 1 possible (and safest) solution for the mite infestation you have based on IPM, but because these are pets and a closed environment that we are dealing with it may be ineffective. You can try to
disinfect the tank and items. The next time you clean, place the turtles in another space and try washing the tank and its materials in hot water. Most common mites cannot survive in water or in high temperature so this should kill them and remove any eggs. Careful not to burn yourself when attempting this.
Do not try to use any chemical or pesticide to remove the mites. This can be a hazard to your turtles and cause damage to the materials in the tank depending on its attributes such as the acidity.