Awesome! I would have chosen steaming, but didn't want to take the time to teach myself. Be sure to take pics for us!
Sorry for the delay but about par for me. Here's what I did. I first bandsawed, carved and whittled a form on which to bend the piece.
The old piece sits flat on the form.
I then steamed the new piece cut to shape but still flat. Here is where you should shape the cove on the top edge. I did it after I bent it and it would have been easier when still flay. I used a 1/2 inch radius gouge and the sandpaper. I have lost the pictures of steaming. I did it on the kitchen stove when my wife was out of town. The apparatus consisted of teapot, a length of hose, and a piece of 4 inch PVC pipe which is not ideal but handy. I blocked one end with a cap and stuffed a rag in the other, around the hose. I steamed it for 30 minutes and then clamped it to the form.
If you look closely you will see two tapered shims (shingles) under the middle. I did that to "over bend" allow for "spring back" when I relieved the clamps. It turned out that two shims were not enough and I did the same piece again with two thicknesses of shims, overbending by about 1/2 inch.
The new piece conforms to the mold unclamped. I had it clamped for a couple of days and then clamped it up again until I got back to the project.
Here's how it looks. The twist is not apparent in the picture but conforms to the old piece and will be more apparent when two end pieces, which seem to be flat, are screwed on.
Not a quick process but a little more precise than carving and once you have the mold and have sorted the variables, you could make several in short order. (Not sure but I think you'd need another mold for the other side. Most of the twist on mine seems to be on the back end. I'm only doing one)
Note that steaming time and spring back are somewhat dependent on species. I used "Philippine mahogany".
I'll be away for two weeks so won't be able to tell you if it passes the final test, i.e. fits the door until then.
Tom