It really depends on the look you want. You could certainly just add a 6" strip to the side of the backing; no one but you will probably ever notice it after it's quilted! You could also add it in the center, between strips on each side. This is more symmetrical, but again probably no one but you will ever notice it.
If you have a contrasting piece of flannel that would go well with the yellow, you could use that for the 6" strip (no matter where you place it). That creates more drama in the back and is more of a "modern" technique. In this case the strip would definitely be noticed, but that is because it becomes a design element!
It is up to you whether you want the strip to be unobtrusive (the same flannel either on the side or down the middle will achieve this) or whether you want to use this as an opportunity to introduce another design element into the quilt.
Edit: To clearly answer your intial question, it would NOT look stupid to piece the backing in the manner you describe!
Edit2: When using flannel for a backing, it's a good idea to make your seams 1/2" (or more) wide and press them open before layering.
Last edited by Prism99; 07-25-2014 at 07:00 PM.