Derek Cohen (in Perth, Australia)
Wiley, I would modify the widest punch you have so that the end is flat. Simply grind a flat face. If you do not have a circular sanding wheel, then use your Tormek.
The nail punches you have are hollowed to avoid slipping on the head of a nail. My concern is that the hollow will cut into the iron rather than peen it over. A wide and flat face will push the steel instead.
Place the flat head half on/off the edge of the pin. Gentle taps around the circumference. You could finish with a wider nail punch once this is done just to even it up (think of a Japanese chisel hoop setter).
Regards from Perth