Love your wall hanging.
If you choose to bind, I would do it in a single color (if you have enough of one of the colors you used, or charcoal).
You can pull the border to the back, just look at a video on self binding quilts or using the backing to bind the quilt. These usually show mitered corners because that's what will show on the front. You can just do an easier corner by binding 2 opposite sides first, then the other 2. Might not look beautiful, but that will be the back. I really think a color binding will frame your piece.
Finally, a long hanging sometimes doesn't hang well. You can use drapery weights, dressmaker's weights (normally used in jackets) or a couple 3 fender washers from the hardware store.