i have made a few lone star quilts- this one is the (normal) way- and you do cut 45 degrees. i think you are trying to over think it- and you are not cutting anything square---the segments will not be (square) they will be made up of diamond shaped segments with 45 degree angles on each end. use some scrap fabric and put together a strip set & try it out- once you cut & lay out a few sections you will see how it goes together & works.