Howdy, I strongly suspect your "back sinew" is actually from the neck. There's a strong ligament running down the back of the neck on most large ruminants. I was taught to call it the ligamentum nuchae. It looks great but is useless for sinewing bows. Now if you could get the same butchers to save the feet for you, you could collect the leg sinews. True back sinew is from deep edge of the backstrap muscle. Since the backstrap is routinely butchered out and separated from the sinew you might be able to obtain that too.
I suggest that the stuff you do have could be turned into a dandy glue. Ron