I was going to suggest just doing the binding, but if the binding is repeating the batiks, it will be a very low contrast quilt. I would add a pure black wide border (or pure white) in there for contrast.
I'm thinking maybe if you cut a free form curve along the outside of the center/inside of border it would add a strong design element that would coordinate nicely with the breezy, carefree design of the batiks. Since the outer edge would still be straight you could keep your pieced binding even if it's SOG.
Cool quilt! I love batiks! It will feel like you're on a Caribbean vacation every time you take it out!