Aye the magnets would work on a thinner material, the ply is just too thick. Card would be fine I imagine. I'm not sure magnets would work that well for storage, I've tried that before and it's a bit hit or miss. I admit I ran with it to get it done than thought about it first.
The only thing which I can think of to fit in a box would be to replicate that excellent Viet Nam Tunnels game which I think some dutch kerels had at Salute a couple of years back. You'need a box with internal, lift-out, trays.
Smaller scales make it more viable I think, in 2 or 6mm it's a sizeable area.
Have to point out how I originally got the idea from IanH
http://www.iandrea.co.uk/wargames/glads/page42/page42.html who originally got it from Military Modelling magazine, Vol. 3, No. 8, August 1973, p520, in an article entitled
"First, take a biscuit tin..." by Hugh Walters. Not sure many articles from forty years ago still live on.