I'd stick to throwing stuff out. Can you get anything like recycled newspaper or cheap paper towels around there? Or just drive to the store and pick up a year's worth of aspen.. Shouldn't be that difficult to arrange it so that the bedding doesn't spread everywhere, really
The thing is, if it's not absorbant, all the waste is going to spread around, and if it is absorbant, it's difficult to get thoroughly cleaned. Plus you end up using money in washing the stuff, anyway.