I like the idea of the straight lines following the lines of the chevrons, but I agree that some curves would be nice. How about making the straight lines at different distances apart, and between some of them put curves of various sorts - circles, waves, spirals, etc.
I love the quilt and the fabrics in it, even if the colors are unconventional for a baby. I think the binding could be in any of the fabrics in the quilt, except the white.