Cuben is notoriously bad for abrasive and puncture resistance. That's the thin mylar films that are used.
I just got finished working with a piece of 1 oz cuben, and even the mylar film on the outside edges of that is pretty weak/fragile. Polycryo is much better in that department.
Btw, nice idea and execution of same. I'm planning on rigging up something inside my Tipi tent, sort of as a liner to take better advantage of the titanium wood stove that goes with same.