This is what I would do. I would make strips of the three layers - backing, batting, top fabric. Make sure the edge of your now sandwiched quilt is straight and smooth and then add the added piece by butting it against the other and then zig zag it to the base quilt. This will retain your 1/4" seam allowance. I think most satin binding is made to be sewned without turn under. I believe the binding should be full to retain both look, wear and some stability otherwise the softer fabric withoug binding will flop in the wind.