I like the idea of using both borders for your backing. It could be a little bit tricky with only 3/4 inch extra width on either side. I think I would find a fabric that matched the outer edge of the border fabric and sew it on just for 'comfort'. If you do not really need it except for stability on the outer edge, it will be cut away in the squaring up process. If you need it, that small amount will probably go into the area under the binding. You could also do this process with the fabric you use for the binding. It would be unobtrusive.