Hey, SwampDonkey, glad to see I'm not the only one with this problem.

I think the solution is easier than you realize. That's because Rubbermaid tubs can be stored outdoors, under a basic lean-to, for years without noticeable degradation. They'll stand up to sub-freezing temperatures if handled gently, they'll keep out rodents/insects and direct moisture, and if they're kept out of sunlight they won't be any worse for wear.

I think you could build a stout but temporary lean-to on the side or back of one of your outbuildings for next to nothing. I assume you have access to wood already. For the roof/sides, you could use asphalt roll roofing, or consider heavy-duty UV-treated tarps. FWIW, I can personally recommend medium or heavy-weight plastic tarps from Integrated Plastics, a Canadian company; they make multi-layer "haystack" tarps that will last for 5+ years in direct sun, and mid-weight forest-green tarps that are good for a couple of years at least. Country hardware stores stock these, big box outlets don't.

As long as the tubs' contents can stand freezing temperatures, and some minor humidity changes, I really don't think you'll have a problem.

To control rodents (deer mice are the usual culprits, and the main worry where I am; they make a mess, and may carry hantavirus), a couple of thoughts:
a) a sheet metal barrier at least 18" high, tucked into the ground if possible, with no gaps
b) a scrap plywood barrier, same height, with a generous 2" stripe of axle grease all around; mice won't cross the stuff
c) bait pails (sealed against kid/pet access) inside the "perimeter"; I find the "one feeding kills" variant of warfarin to be highly effective.

Away, that's my two-cents' worth, and a bloody long post to boot. Hope this stimulates the creative juices, and helps restore domestic peace and harmony.

Cheers,
Doug

BTW, I'd drive a thousand miles for your garage/yard sale. I can hardly imagine the amount of cool stuff you'd be getting rid of. Make sure you post pictures (if not directions).