You can add Cornerstones by using the Applique method. Do not take your fine work apart. Cut tiny squares with quarter-inch seams, which fit perfectly into your intersections. Then, turn under the seams, and hand-stitch them in place. Personally, I would not attempt to machine stitch them, as it would be tedious and boring for me, trying to wad and twist a big quilt up under my sewing machine. Applique is the Way! Good luck, and enjoy whatever you do.