Having made several on point quilts, which is the same as making bias blocks, I would say adding your off white on grain would help stabilize all the bias. You just have to be very accurate in your cutting and your seams. When sewing a bias and an on grain together, I put the bias against the feed dogs and the on grain on top. The feed dogs will keep the bias from stretching and bubbling. BTW, I love your pattern. I have some William Morris jelly rolls I have been itching to use. But like you I hate to cut into them, they are so beautiful.