What I did was to store my boxes in the three foot high space over my bed room celling. You can cut an access trap door through the celling or build cabinet doors through the sky light soffit in the bathroom, as I did.
You will need a ladder to get to them and I stored them in heavy duty builders trash bags and sealed all with duct tape. Use a marker to label each bag and record the contents along with each bags location in the celling in a log book.
Or you can just get the dumpster! 
What ever is more fun. 
