The "offset stripe" problem plagues those who make hand-stitched kilts as well (just look at the back of kilts at Highland games, and you'll see that lots of people don't get it right there, either)! The best solution, as Steve says, is careful offset and, for machine stitching, holding the fabric tight and taught. If the fabric is under tension from front to back as it feeds through the machine, the top layer is less likely to crawl. And do all the things with the feet and the feed dogs that you can. A quilting foot can help, which is maybe what you already have.

Barb