What is the weight of 3/4" mule tape per foot? I'm not sure how multiple strips would be for distributing the weight evenly across the back of the tree. Also, I am under the impression it is rather stiff, making it something of a challenge to fold and sew, if that's what you have in mind.
All the Cuben fiber laminate I've seen has had fiber reinforcement in either two directions or four directions. They may make unidirectional Cuben fiber tape and THAT might be interesting. Otherwise, my impression is that you would likely be using one of the heavier Cuben fiber cloths (1 oz or heavier) to get any sort of durability, but it's worth looking into for sure.