Ooooh, pretty block, but you are asking for odd fractions.
With a 9" block, each section of the 9-patch is 3". which makes each piece 1" wide.
With a 12" block, each section of the 9-patch is 4". which does not compute well and comes to 1-3/8" or 1-5/16".
I would suggest keeping each strip 1" and adding another strip on all 4 sides, making each section 4 strips at 1" for a total of 4". You could play with the color combinations and come up with something really nice. Does that make sense?
Hope that helps.