I tried covering the door panel a second time. With my first attempt, on the left below, outlines of the clips that hold the panel to the door show through the final product. I believe that the clips are made of wire rather than sheet metal and are therefore too thick. On the right is my second attempt. I stripped off the vinyl cloth, added a layer of 1/8 inch foam, and then recovered the panel. A big improvement, but not yet perfect. One can still see a faint outline of the clips on the left edge. I think I will leave the panel as it is and move on.
The kick panels were next. These are the coverings in front 
of the doors and under the dash. You can see the place that is hidden behind the panels in the picture on the left. The white paint on the interior side is the original color of the car. I don’t know what the brown color is other than not rust. The same coating was on the back side of the panel. Perhaps it is a glue or water seal.
The original panels were a thick cardboard covered in a thin vinyl and had seen better days. Because the cardboard had bends and curves molded in to fit the shape of the car, I couldn’t replace it with wood as I had done with the doors.
But I could fill in the holes and add some strength by adding epoxy resin and some fiberglass cloth. I had these materials available from my Factory Five 818 project and had some experience with them. 
I mixed the resin, applied it to the weak parts on the rear of the panel, and then added fiberglass to fill in holes. After the resin cured, it was easy to trip the threads around the edge.
Here is the left panel, covered with the same vinyl as the door and installed. A big improvement, but not show quality.
Sunbeam 