I've got an idea that may interest you.
When you sew these strips together. and then cut the edges creating the triangles, you will have bias edges all along the outside edge of your quilt. So......
Try this trick of using 1/4" twill tape within the seam allowance to stabilize those bias vertical and horizontal edges. Twill tape comes in little packages like rickrack; you need several depending on how long your borders are.
Jan in VA