your second idea, split down middle and add a strip, was the recomended method when i learned to quilt in the 80's. the thought was, that the back was stronger by having seams to side and solid strip in center. but since then, methods and thoughts have changed. no rules ...i am in love w pieced backs. backs made w leftover blocks, backs made scrappy style with big chunks of fabric left over from piecing the quilt. do what is fun ... it all works and looks great!