I've found that a zip lock bag takes far less space to store.
With the big ones, and you can put your spare parts in there, as well as the instructions. Label it,
I usually cut one of the smaller images on the box and toss that in there too.
You can get 30-40 of those baggies in a tall ship box.
If you're adamant about keeping the boxes (I've never been), the just fold them flat and slide 'em behind, under, or over something for storage.