You can cut strips of batting to "fill out" the binding. I would probably zigzag the strips of batting to the quilt's edge, then fold the binding over to the back. No one but you will ever know about the extra batting.
The one thing I'm not sure about is if the miters at the corners will still work. I think they will as long as your added batting strips are all the same width.
If you want to be sure, I would cut a couple of batting strips, loosely zigzag a few inches of it up to a corner, cut the strip off even with the quilt edge, then loosely zigzag another strip from that corner a few inches down the next side of the quilt. Fold the binding over to make sure the corners will miter correctly.
Edit: Theoretically, what you are doing is extending your quilt's edges to accommodate your wide binding.