I agree that another layer of sashing would add interest. If Im undersatanding the current sashing color it Is a warm grey that has muted purple/mauve tones. Instead of going for a pop color I would go for something darker to let the checkerboard shine. You said there were alot of dark blues in the fabric so I'd look for a dark blue or purple. I drew out a quick sketch so you could visualize better. I also choose an off white border to let the eye go do the white and black in your blocks.