The couple of bows I've sinew-backed, I used deer leg sinew and pulled it apart into really small pieces. Backstrap sinew would work, but the leg sinew seems a bit softer. If I was gonna sinew a shorty like that, I would put at least three courses on it. It'll probably take at least two or three pieces to do each course, maybe more depending on how long it is. The pics I've seen of the cross sections of the short plains-style bows, the sinew is usually about a third or fourth of the thickness of the wood.