Is the quilt now yours or does it belong to your friend? If she says "it adds another story", it sounds like she wants to leave it as it is. She does need to be aware that this is fragile and needs extra care/not heavy use though and it isn't going to take to frequent laundering. It has now become a "display" quilt and not a "use" one. You do know that any fix will diminish the quilt's vintage status?--if that is of any concern. Adding today fabric may be too bright for the age of what you already have, too.
Isn't there another product now that is similar to Fray Check that leaves a softer edge? Fray Check can leave a hard surface.