I haven't read all the other comments, so hope I am not repeating. Also, I am not familiar with Jo Morton's quilts. From Googling, I assume they are normal pieced quilts (not miniatures). If so, my comments should be relevant.
Being exactly on grain is not all that important in quilting. You can be slightly off-grain cutting without affecting the quilt. If you want insurance, you can heavily starch your fabric before cutting. Starch stabilizes the fabric so that the pieces (especially the edges) are less likely to stretch or distort with the handling involved in piecing.