How about black binding around the red edges and red binding around the black edges? It looks like you could do half-and-half. There'd be one block with a red edge that would get red binding, and one block with a black edge that would get black binding, but I think that would just add even more character.
I also like bias bindings made out of striped fabric if you can find it. I actually think the idea above, though, is more in keeping with the color-block nature of the quilt.