Ok, so several options -- we can do this.
First off tolerances would be tight and it would be a lump along the edge but you have enough left on the one side to cut into a strip for the other side. I'd consider cutting the remaining strip into a long skinny triangle and off set it a bit to get the other length instead of cutting two super skinny strips.
Likewise, I don't think you have quite enough but you just might be able to cut your existing piece into triangles and slide them down just enough. That would leave a large undesirable seam in a large scale fabric so not your best choice maybe, but a possibility.
http://blog.ilovefabric.com/2009/03/...-flynn-method/
Next option -- any white flannel in the stash? Or a color that otherwise goes with either the top or the back? When adding fabric in cases like this, I like to make sure stuff fits easily, so I'd actually trim off a bit from the width and put two edges on, about 8" each, so there would still be a couple inches to quilt with. Normally on back seams you do cut at 1/2" and press open. In this case, I'd still have a 1/2" seam but I'd fold the flannel over so the fleece lies flat -- if that makes sense.
Here's a "more fabric" option. Add a border around your top and make it bigger! Then frame the fleece with same fabric, and bind with the same. If you aren't using batting, consider a layer of flannel or very thin batting in the cotton to cotton sections.
My first attempt at using fleece had a piece that turned out just a smidge too small, and I pieced in a bit of the coordinating binding fabric. Not ideal but you can see a triangle about 1/2" wide x 3 inches long and it made it possible to finish. Once done you really have to look for it. You can see the back side of the cotton pieced in fabric in the photo.
Edit: The final choice is to simply design and make a new top for the hedgehog fabric and use the existing top on a different back. I'm really rather notorious for changing my mind and making a different back for a project which then means I have to find a project for the rejected back. With some of my fabrics that can be more easily said than done!