I have lots of tricks to use less fabric for the binding.
First: you don't need 15 inches for the corners. You actually need nothing extra. The length of the binding is exactly the length of the outside measurement of the quilt. You just need to add enough for the final seam overlap, which can be the width of binding or less if you're willing to figure out how to do that.
Second: I don't do the complete 45% angle on the seams. I lay my strips on the cutting board, lined up with a line on the board, over-lap the strips one inch and cut the diagonal from the point of one end to the opposite point of the other. Pick them up RST and sew that seam. The seam is still on a little diagonal and will not produce bulk, which is the reason you cut those seams on the diagonal.
Third: You don't really need 1/4 inch seams. Ask Ricky Tims about that. A 3/16 inch seam or even a little less will hold just as well there.