Thank you all SO much for your input and all your great ideas and comments. Yes, I washed the fabric first, it is 100% cotton and the design is printed on, not woven in. (I knew that the printed design is not really to be considered when determining straight of grain, so I usually avoid buying obvious, predominant stripes. Once this fabric is cut and pieced with others, the stripe will hardly be noticeable - just the overall design.)
I've always been afraid to straighten the grain by pulling the fabric - I figured it would just return to it original grainline through handling and laundering, but I guess I was wrong. I will keep this in mind the next time the problem arises with a fabric whose design is woven in. Thanks for reminding me it's OK to do this.
In the meantime, I am going to stick with my original idea and just go by the selvages. I am very comfortable with doing it that way, and it seems to work for me, so I guess "if it ain't broke.......".
Thank you again. I knew the great people on this board would point me in the right direction.