I have tops that have been stored for years and have had no problems with bugs. I would tuck them into old pillow cases and put them on a top shelf of a closet.
Putting them in a plastic container can cause moisture problems because humidity can't escape.
Moth balls are another questionable item. They are very poisonous and smelly. They will discolor fabric and the odor my not come out.
have fun in your adventure with HH. Amazing
peace