How much yardage do you have? 4 yards?
Do you not want a straight seam? But you want to use the one fabric for the back, right?
Sounds like an opportunity to use John Flynn's diagonally cut backing solution:
http://www.flynnquilt.com/media/uplo...nalpb1103.pdf/
Yes, it's scary looking. Just remember - he's an engineer. ;-) But it is decipherable.
here's another post with a review of the method:
http://bsue.wordpress.com/2007/03/25...ng-directions/
I've never used it as I like multi-fabric pieced backs but I've always kept it in the back of my mind just in case I found myself in your exact situation.