I threw in the towel on finding good used doors locally and bit the bullet by cutting out the rust and welding in new sheet.
Cut a piece of 16 ga sheet and bend and pound it into shape.
Check the fit often
Out with the rust, in with the new
Tack weld and then fill in the gaps. If the metal warps, peen the weld bead with a chisel point hammer across the bead to expand the metal.
Grind, fill, sand
Paint
Done. It needs some finish filling and sanding before the top coat is applied. About 4 hours, total, not including the time for the filler and paint to dry.