Jen, since you are giving these away for free I've moved this thread to the "Free Stuff" section of the market place.
Maybe there will be people that take them away. If not - don't sweat it, just put them out with your next cardboard collection. Depending on where you live that means you'll be storing for up to 8 weeks
When I moved a lot of stuff recently I bought a whole lot of packing boxes from a freight forwarder near the airport - wasn't very expensive - just a few francs each. They were boxes for PC monitors - the companies must sometimes make too many of them.