For the most part, I think that the earwigs only hide in the cabbages since that's a nice dark and damp place. However, they will chew a bit to make a nice snug home. I could probaby live with them if I were not in the middle of grating a head for slaw and later seeing half of an earwig crawling away!
I don't store cabbage since I normally only plant enough for fresh slaws, fresh cooking, and a bit of kraut. However, mother-in-law used to grow a real late variety and simply stack them on shelves, cut end down, in an unheated basement. Once the outer leaves dried, it seemed as if they lasted all winter. I've never tried it but may do it with a few this fall. I felt sorry for all of the seedlings and planted twice as many as we can use!
Martin