I was thinking the same, maybe hardboard or pegboard. Styrofoam would be light but not having enough - any? - tensile strength.
Styrofoam, haha, yeah good luck with that! Pegboard might work. I wonder if the holes would produce any wind drag? My paddle weighs about a pound and a half. Let me know what you come up with!
When I was first pondering the construction of this thing, I briefly considered aluminum (maybe with L brackets along the sides for strength), but then I decided that my metal skills are not good enough for that.
For a while I thought about attempting to redo mine, but ultimately I decided that the weight of the wood is really nothing compared to the water that you are going to put in the bag.