At least with wrought iron, you can heat it indirectly. Use a big chunk o' iron for a heat sink; heat it up, then use the heat sink to heat up the sheet metal. My first few welds were done that way. If I remember right, we used a chunk of railroad track about 3-4" long for the heat sink.
I don't think you'd need a swage, just the mandrel. Work with stock longer than you want to finish with, then trim afterwards. You might try pre-heating your mandrel so you won't lose heat so quickly.
Wrap the sheet around the mandrel but not quite touching, then remove it and set it to the side. Heat up your heat sink and pre-heat the mandrel. Put the sheet metal "blank" on the heat sink til it looks sticky, then pick it up with the mandrel. Flux it, tap the joint, and it should weld.