I know they are very small, but they will cope better than the mites. If you need to put in some small bits of leaf for moisture then don't leave them long, so you don't feed the mites..... I said you can save them. Depends how bad the infestation is, and how much of the mite pop. you remove when you get the dead crickets out.
They are obviously the main breeding ground for mites. Mites also love :- any meat, potato, carrot, in particular. Fortunately, they don't seem to care for leafy greens much, so I think you can get away with this one........