If you have a fully charged good 6v battery and it won't turn the engine fast enough to start there is an issue. Dirty greasy starter? Bad connection especially engine to frame ground & battery to frame ground. The starter may need a good cleaning, commutator cleanup, brushes? The starter could be drawing so much power that there is not enough for good spark especially through old questionable parts & connections.
It is safe to run a 6v starter on 12v if you are not making long cranking runs. The problem would be that unless you remove the main power feed 12v will be running through the whole system and some stuff won't like it. I think it would be better to add more 6v amps by connecting another 6v battery or booster in parallel with your battery.
You cam check spark to the plugs by simply removing one & grounding the base on the engine and cranking with the ignition on. My dad used to just grab the plug wire. HEI ignition and a magneto on one of my flatheads broke him from that.
