ok, I am no expert quilter, but the math wiz in me says you can turn this on point without adding extra fabric. You would turn your square quilt into a rectangle though.
Here are the steps (please excuse crappy photos, I just did this really quickly with my web cam and a post-it note).
1. Mark the centre of your quilt by chalking a straight line horizontally and vertically, point to point (see photo 1).
2. Fold down the top point to the centre point you just made and likewise fold up the bottom point to the centre point (see photo 2).
Mark those fold lines and cut your quilt at those lines. (see photo 3)
3. Cut each of the small triangles you just made in half along the first chalk line you made when you marked the centre point of the quilt. You will now have 4 smaller triangles.
4. Fit those 4 smaller triangles along the right and left sides of your quilt to make a rectangle. (this is photo 4, I will put it in the next message).
More experienced quilters will have to let me know if this will work or not. The other thing I can't visualize is how the squares will look in the triangles you cut off and re-attach. They obviously won't be in the same order or orientation as the main part of the quilt but it could be a cool effect.