You say this is a special quilt for you Grandmother. Have you considered a pretty hand quilted motif in the white squares? I have mixed machine and hand quilting in an irish chain and it looked great. It doesn't take long to hand quilt a few squares and if you are not comfortable with your handquilting skills try doing big stitch and keep the pattern simple. Lots of ideas on line. You could do a heart or a simple flower and make a template out of cardboard.