My two cents:
I used a u-haul in my driveway for tool storage when I finished my garage, and even in December it was hot and a bit humid.
External storage containers / trucks / etc. are not guaranteed to be dry. Even if they don't leak, many storage solutions will not be insulated and could condense. Moisture inside, added with heat, is a bad situation for any manufactured wood. I can think of all sorts of crazy solutions with desiccants, insulation, forced air, layered tarps, but it just seems like more trouble than it's worth.
Given that you absolutely don't want them to leave the property, and that you have to move them no matter what, why not buy a bunch of the harbor freight furniture movers, shrink wrap/blanket all your games to protect them from dust, then set them on the furniture movers and wheel them around the garage as needed? Throw a giant tarp over all of them if you are worried about the workers messing with them, ratchet strap in place until you need to move them to the other side of the garage.
If properly wrapped, a bump here or there won't hurt them, you'll keep them secure, and you'll have minimal moving to do when your done. You'll also have a bunch of furniture carts you can use to sponsor a drunken soap-box derby.
Edit: And since you asked, I HAVE used this approach inside when I was repainting. Worked great.