I'm into this late, but originally those were made from heavy cardboard (3/33" thick) and the door handle and the window handle had a foam rubber washer keeping the panel pushed away slightly. Between the handle and the panel was a durable plastic washer. There was a metal perimeter frame. That washer did produce a bulge, but it wasn't unsightly. That foam rubber is exactly the stuff mousepads were made from and the same thickness. If you can find one of those old mousepads it would be perfect to use. There was also a thin jute fiber piece which mounted over the door handle rod in some years, but it didn't last long and you almost never see one still intact today. It was to keep that rod from rattling (which it will do). You can make one out of 1.5mm thick leather which will outlast you. Cut it about 4 or 5 inches long by about 2 inches wide. Fold it over the rod about 10 inches from the door handle and staple it together a couple of times at the bottom. You probably could use thick naugahyde also. Lacking that heavy cardboard, you can also use Formica counter material (which works well, fits into the frame, can be covered with vinyl if desired and will not shrink nor warp. Good luck.
