I too am a binding "traditionalist" and prefer to machine sew my binding to the front and hand sew to the back, I just think it looks much nicer or cleaner.
However, I recently had a LA client who wanted me to do a backing folded over to the front binding by machine. I used one of my Bernina's decorative stitching and have to admit it looked pretty darn good. I suspect you could do the same with an attached binding. Match up your raw edges and machine stitch to the back of the quilt. Fold the binding to the front, pin and sew down with a decorative machine stitch instead of the standard straight. I lined it up so the edge of the binding was right at the center line on my presser foot (I used a walking foot just to be safe and not get any puckers). A small zigzag may also work but I would test it. My decorative stitch was a leaves and vines and because it serpantined back and forth I was assured of half the stitch being on the binding and half on the quilt top.