Hi, there -
When I first read this, I thought you were considering washing the binding fabric after it was cut. But you are asking about washing the binding fabric as a big piece, with zigzagged edges (I think).
Wouldn't it also work to cut the binding and then run a stitching line of small, straight stitches, using a thinner thread like Aurifil, to stabilize the edges while you are sewing it down? I'm doing that now with some very trying fabrics that not only fray but STRETCH, and it's working well. You could even sew the lines down at the proper distance from each other and then cut afterward.
Just an idea . . .
Charlotte