I hang my wool one(s) in a garment bag in the closet on a 4 clip hanger. I have a few cedar balls in the bottom of the bag to keep the moths away. The PV ones I also hang. but I fold them differently.

Lavender sounds like a good idea as well. One question though. Doesn't lavender attract scorpions? If so, I wouldn;t suggest it fotr people where this could be an issue