you can always use the extra to make pilowcases or a wallhanging

If it's a deal breaker, and you can't use it, then don't use it. Find a different backing fabric that isn't directional.

I have to use this fabric, this is what the man who commissioned the quilt has picked out. I did try to find something else with these colors, but nothing as pretty could be found. I did some recalulating this morning, I am pretty sure I can do this with only 12 yds - not 16. So I am going to JoAnn's today to use my 50% coupon.

Couldn't you buy a bolt and say 4 yards. You would still have extra but not as much extra and could still get the size pieces you need.