I learn a lot every time I quilt something with different quilt line needs. I've decided that when I really need perfectly parallel tightly spaced straight stitch lines ... I might first use my open toe quilting foot 'toe' to trace the line just quilted. So in this preparation sample... the left 'toe' on the pressure foot is my guide as I stitch in this case from left to right moving forward ( north to south) and and backward (south to north) creating a parallel grid.
In a different stone piece prepared the same way as above, it is pretty simple to keep the rest of the fill nice and straight as I move from right to point of origin on the left. Another benefit of this method : Much less chance of creating an excess wrinkle in the rug on one side of the stitched area. Yeah!