Sounds like your battery is toast. A single starting activity should not be draining the battery to the point where it's unrepeatable. Check the aforementioned cables, connections, etc and put that battery on a charger over night.
Keep in mind that it's the battery's cranking amps doing all the work when turning the engine over. Switching over from 6 to 12 volts may not actually result in an increase of cranking amps depending on the battery you purchase, so it's not as simple as that.
Food for thought. If you want to do a little light reading, here's a story I wrote for Hot Rod Magazine rewiring and converting my Model A to 12volts. Hopefully you'll find something useful in the story...
https://www.hotrod.com/articles/upgr...-a-12v-system/