Good thread. I've spend many hours wrestling with plant fibers instead of sinew and here are my observations so far:
ALL the plant fibers I've tried will stack sooner than sinew and will not allow draw long lengths without damaging the back or the belly.
The flax I tried was quite weak and I think it was due to the fact that it was retted too long. The other fibers were obtained from commercial twine or cord: jute, sisal (which is actually the same as agave), cotton, hemp, and manila fiber.
Nylon may be the answer but I still haven't found a good way to glue down individual strands as opposed to nylon fabric. Some say hot melt glue will work well with nylon but I haven't tried that yet. Seems like it would be very difficult over a large area, so I put the idea on the back burner.
Hide glue seems to work best. Knox glue also works. Fish glue is too brittle unless you make your own from fish bladders. Titebond also works well but it does not spring back as fast as hide glue. It will eventually pull itself back into shape, though.
Seasoning and processing my own fibers has always worked best for me and anything that can be used for a bowstring can be used for backing. And I never cut down long fibers before I put them on a bow. I put them down in the longest strands I can get and I toss out the short fibers. I also found that combing the fibers throughout the process makes a BIG difference in how they lay down.
As a final note, all fibers dry in different ways and some will not lie flat when drying unless you wrap them down. So, as a default procedure, I wrap everything.