I store my ammo in old ammo cans that I bought at the army surplus store for ten bucks apiece. The olive-drab NATO kind that seal up like an old-fashioned mason jar. It never occurred that moisture could get into them anyway, especially since I live in an environment that gets very humid in the rainy season. The cat litter in pantyhose sounds like an excellent idea. Using rice sounds like a great idea, too. I put dry rice in salt shakers to keep the salt from clumping in the humidity, so it should work just as well in ammo cans.
I've got over a thousand rounds to store. I need something very effective and at a very low price.