I'm gonna say, that backing isnt doing you any good all tangled up like that. It needs to be straight laid down, like the strings of a guitar, and laid directly side by side. Also, if the bow has survived this far, you probably dont need a backing at all.
Ok, gonna modify my reply a bit after rereading your post. Because you decrowned the bow, and I dont know if you followed the grain or not when you did it, I cant say whether you need a backing or not. When done right, a decrowned back doesnt need a backing at all.
I still say that your fibers currently on there are doing absolutely no good. I think you should peel them off, sand the back down smooth and give is a picture of how the rings on the back look. That will determine if a back is needed or not.