I took everything out of the closets and aired it. I am pretty careful to wash everything before it goes into storage for the season, so I've been adding loads of winter clothes to my regular laundry here and there. I probably ought to clean the closets, too, but I'm on to outside projects at the moment.
After a little research, I came across a way to repel moths with a herb/spice mixture. I used a quarter of the original recipe.
1/2 oz. dried rosemary (about 3/4 cup)
1/2 oz. dried mint (about 1 cup)
1 Tbsp. dried thyme
2 oz. whole cloves (about 1 cup)
Place mixture in tea sachets or fabric bags. Hang in closets or tuck between layers of folded clothes.
I made some hanging sachets as well. I put about 4 sachets in each closet that stores clothing and quilts. I plan to air the contents of the closets in the sunshine at least once this summer, and I intend to thoroughly clean the closets at that point, too. Let's hope it works!