Personally I would use a knife-edge finish, aka turned-edge. There's no additional fabric to add, the seams of the front piecing are not an issue, the front piecing goes right to the edge of the front and the backing fabric goes right to the edge of the back. Very neat and clean looking. It's one of the oldest methods of finishing a quilt and can be quite sturdy.
http://welshquilts.blogspot.com/2011...nife-edge.html
This example does not wrap the top over the batting before stitching the top and back together, but I have and would in your case. It adds to the durability of the edge.
If that's not an option for some reason (e.g., already quilted too close to the edge), I'd go with wrapping the front to the back despite all the nay-sayers. I've used 1" piano key binding (single fold) and it was not all that difficult despite the seams.