you don't necessarily need sinew to up the poundage. In fact, sinew is far to elastic for such a light-weight wood with moderate compression capacities.
You know coarse sisal fiber cordage that's used to bind together small bales of hay? Cut it into pieces of 10" or 25 cm, wash it, comb it, dry bundles flat on a towel, and use hide glue (or gelatin) to back your bow with it. First toast the belly, and treat the fiber otherwise as sinew (but instead of stretching 5% it will at most stretch 1.5%, which is more than you'll ever need on such a bow).
You'll need about 10-12 m of rope. String the bow backwards before applying the fiber, and after gluing wrap the limb with strips of the inner tubing of a bike (make sure not to overlap, let the fibers breathe). I typically let it cure for a few hours above my stove (at 60-70°C) so the excess hide glue is pushed out by the rubber, and next it dries. I wait for a week or so to let the entire limb cure in a dry place.
