High humidity in FLA is a bear. It can be done, but you mustn't strip the seasoning off by using detergent. I ran into that some when I didn't have AC in southern FL.
Any chance you want to sell some cast iron HolyBus??
Family wagon- desiccant sounds like a decent idea. I'd want to check the litter ingredients, and likely wouldn't want to store it on the cooking surface, but I bet that would work! I have a long tent camping trip coming up where it almost always rains. I'll give it a try!