I would also use the stripper. Get the stuff from the parts/paint supplier, not from the local Home Depot, unless they carry Aircraft stripper.
I just got done stripping the door jambs, rocker panels, trunk opening and rear body panels of my 67 Stang. I masked the jambs to protect the interior, applied the stripper, let it work for about 30 minutes, scraped the excess off with a scraper, used steel wool on them, wiped them down with laquer thinner, then went over them with a wire brush on a die grinder. Total time involved from paint to bare metal was about 3 hours. That included a couple of breaks to wash the stuff off the skin! OUCH that stuff really burns!
Make sure you wear protective clothing.