I like to have one piece borders as well. I measure the center of the quilt the long way and cut the pieces on the lengthwise grain and sew them on. Then I measure the shot sides. I learned to do this many years ago -- the fabric does not have to be as long when you do it this way. I know the short sides may be a bit stretchier but if I starch enough it is not a problem and the stitching will hold it.
Even if I don't have enough fabric to do the full length of the border in one piece, I always cut my borders parallel to the selvage since that direction is the least stretchy.