Except for where the top and bottom seams are going to hit, which would make quilting more difficult, I wouldn't worry too much about how you piece the back of the skirt, or actually what you are going to use. I know you already purchased the backing fabric, but I would have gotten a piece of 108" muslin, or used a sheet, thrift store or new.
I do have a 'thing' about spending money for backing fabric. I look at how the item is going to be used. If it's going to be put somewhere, and not really moved around a lot (bed quilt, table runner, tree skirt, wall hanging etc.) I am inclined to use something sturdy, but less expensive than LQS quilting cotton: nice quality muslin, coordinating sheet, scrappy etc. If the item is going to be thrown around and used a lot, where you are going to see the back almost as much as the front (throw, baby quilt etc.) then I spend the money and make the back out of something really nice, or take pains and piece it nicely.