Alright K--I just found this thread and of course, I want to throw my own 2 cents worth in (maybe 2 Euros worth?)
When I looked at the picture of your door I envisioned your quilt hanging close to the door (like Butterflywing said) to keep out as much draft as possible.
If I was making this quilt I would put a hinged rod on the alcove wall on the right side of the door (the wall on the kitty door side). Then I would make the quilt the length and width of the door wall-ceiling to floor--2 sided. At night you can swing the rod around and it will cover the door-your cat is certainly smart enough to nose around the side and find his door. During the day you can swing the rod open and will have the back side of the quilt hanging against the wall (a pretty for guests to enjoy as they come and go). If the rod will extend too far out the wall because the door is wider than the wall, then you can get a rod that is telescoping and can make it a little shorter during the day. If you are worried about the weight of the quilt then you can put hooks on the walls at the non-hinge end of the rod for support. Your quilt can then have a rod pocket on the back, can hang from clips, etc-how ever you wish to hang it from the rod.
This is just another idea for you to toss around in your head. If you need a rod they sell them at Bed, Bath and Beyond and I would be more than happy to mail you one......