This is exactly what I was thinking just a few moments ago. I think, though, since this is a gift, I will use the backing fabric I have left over. I like your idea of using muslin/re-using it. This would work for quilts at home I am rotating for display.

I will give this careful thought. I've never used monofiliament, but it is an intriguing idea. Thanks!

Hum...your vertical strips idea, in particular, is intriguing...I will definitely think about it. Thanks!

Yes, I've concluded this may be my best option. Thanks!

I have several quilts on which I put a hidden sleeve. I have to point it out if I take it to a show. l quilt it all except the top border. I put a folded piece of thin trash fabric at that top between the batt and the back. I then quilt the back and that half of trash fabric, and next quilt the other half of the trash fabric with the batt and top. I put a little good fabric at the very ends that might show in use. Then the binding goes on, being careful not to catch the sleeve fabric at the ends. These are quite invisible in use.

Another thing I do is a camouflage type of sleeve for the back of the quilt; it takes some pre-planning though. I take the backing fabric and sew a sleeve (depending on the circumference of the stick/pole/hanger/rod) I cut a piece of the backing 3 times width of it. For instance, if your rod measures 2 inches in circumference, and the width of the quilt is 40", I would cut out piece of the backing fabric 6" x 38". I would sew a small hem in each of the ends and then fold it half at the length. Now your sleeve will be about 3" x 37". When I sew on the binding, I would center the sleeve at the top of the quilt and sew the binding over it and bind as usual. Now you have this floppy sleeve at the top of the quilt. I then hand sew the sleeve down at the bottom of the sleeve.

So now you have a sleeve automatically sewn into the quilt at the top. It does not show because the sleeve is the same fabric as the backing of the quilt. This now gives you the option of either hanging the quilt or just using the quilt as throw quilt. Most likely no one will ever see the sleeve.