Marlow
if it just fell apart into short strands, I just gotta wonder if putting that much twine on with TB3 is getting you all that much protection compared to the weight you are adding. I have a hickory board bow that I backed with linen cloth and tbb3. It looks nice, shoots just ok and has not broken, but I do not know if it would have broken without the backing, or whether it would be a better shooter without it either.
I have played around with some other high strength backings for composite designs, and came to the conclusion that less is better. I have also used maple as a backing, and wish I had access to some nice hard maple for trying in a trapped back.