I store my side ways because I can't even imagine the inconvenience of having them stacked on top of each other. Now that I think of it, my upline stores hers flat and she struggles when she's looking for a certain set.
The wood shouldn't warp. If your in a climate controlled area, the rubber shouldn't be affected. If the rubber and adhesive were in a warm environment, I could see the rubber sliding off, but mine stay in my house, so it doesn't get that warm.
My husband build me a shelf that fits each SU container perfectly--and there's no waisted space. There's a pic
here!! HTH!!