One of the purposes of a binding is to make a frame for the quilt so the eye stops 'wandering'. Therefore, I would not choose white. Why not 'google vintage fabric' and see if you could find sellers of vintage fabric. I know there is a shop in Leadville, Colorado, that only sells vintage fabric, linens, patterns, etc. That way, you might find a great match. How about a fabric with just a tiny polka dot? Your quilt is a treasure and I know it will be special over the years.