Approach to Creating Draping Material with a start and end point

Thanks for all the help so far but here’s the hard part. With all the help I have gotten to here (OK, a couple of bolts are still to do):

I would like to get a suggestion on how to create the buckler covering over the frame that looks like this:

Here is what the buckler looks like expanded:

I have measured plans for all the pieces of material. However, as this will be shown in a collapsed state, as in the photograph, I suspect I do not need to go that far. I need an approach for creating material draped over the frame.

I need to get something that starts out as a circle then goes to two ellipses (different size) connected by lines, with draping in between.

(Since nobody else replied yet, I’ll suggest something) Have you already tried making a cylinder, exploding it, and then using the Rebuild and PointsOn commands yet? I think if you drag the points, you should be able to manipulate the surface into a draping shape. By your comment, I’m assuming that you don’t want to have as much accuracy to the details shown in the picture, so I hope this helps. If that doesn’t work for you, then try playing around with the Drape command or using Grasshopper.