I'm about to tackle the same job on my Dad's '31......................
I would go the other direction and LOVE this car! At the very least it did not burn you, your dad, the car, and the station up from the leaking gas and the melted wires, both probably your fault.
Don't be discouraged.
By the time you get the new parts, sat, the wiring from the terminal box to the dash and the wiring from the cutout to the terminal box and a new ammeter, you'll have cooled down a bit.
Take a look at ign sw terminals behind the dash, is that where they arced or shorted?? Cover with electrical tape.
A short at the ignition switch to tank should only stop the coil from working and possibly keep it turned on full time, which can overheat the coil and burn it out, but it shouldn't heat the wires to the switch, unless the coil internal wiring shorts out. Could the gas have melted the plastic nuts on the ammeter? A short in the ammeter can lead to burned wires. Is the ammeter a repro, or original?