I recommend pure hide glue. The fastest glue as it sticks when colling down.
Than wrap the sinew layer with some rubber tape (best I found till now was rim tape), apply some mild stretch, reheat the whole thing and let the excess glue to melt out. After cooling down, unwrap and smooth the surface. Gives a backing with less glue in it. I rarely had some crackling noise when stringing and pulling this this bows for the first time.
Sinew and hide glue - thats like ham and eggs, like man and wife, like..., just a incredible pairing!