I often keep projects for extended periods, often travel with projects, and I hate ironing, so have developed many technique to keep stuff flat! My Labyrinth Way blocks were huge and I used the foam core and clips just a couple months ago
If you are concerned about long term storage, acid free/archival tissue paper is pretty easy to find (and a lot cheaper than archival cardboard). Simply line the box with that -- you don't know what your cardboard has been made from, some cheap woods are more acid than other but I don't worry too much with food grade (like pizza boxes).
When I worked for the engineers, I always had (used) foam core available and other goodies like rolls of drafting paper or whatever. And the hubby worked for a (fancy) cardboard box manufacturer and I got spoiled some more. Now I am back to finding things for low prices and chopping up boxes from Costco.