Have you done much with checking out the arguements for sinew backing Juniper?
I imagine that braided line would work, but I can't imagine it would come close to being as good as the sinew. Sinew and juniper are an ideal match. For what you are getting out of the fishing line, I'd bet you'd do just as well to use some silk from the fabric store, and it'd be a whole lot easier and looks much better, probably.
Anyhow, good luck with it!