If it doesn't fit either way around then I'm not sure how it can be made to fit and still look presentable. The listings are generally sewn along with the section edges. Each section should also be the correct width front to rear. Now if the sections were too wide, the stitch lines may not show after correcting the section widths.
After removing stitches, the old stitch line will likely always show. I'd be surprised if they didn't show. It would be much easier to just purchase a new correctly fitted head liner.