I finally got around to spraying all the door panels and installing them. Especially the front ones needed about 8 coats to cover the burned-in dirt... They got a little wavy when the paint hadn't dried yet, but that went away once they were installed. I also started on the seats, but that's a lot harder than I thought. I can't wait until they are installed, though.
I reinforced the the panel with some glued-on business cards. I hope it helps at least a little bit.