Here's how I am thinking it could be done ... and something I have been considering for awhile.
...... make a really wide binding strip!!
You could do it two different ways ....
* sew the normal seam width of a binding, then flip the large extra over, pin in place and machine or hand stitch in place.
* or sew the large section in place and then flip for the narrower binding to be where you would hand stitch to.
The problem I see with both, would be the wide portion would have no quilting to hold it in place, and might start looking a bit undesirable with washings. I guess you could do some machine quilting after the fact.
On the upside, it'd be a good way to extend a quilt top in length and width.