I am doing a restore on this motor and someone else started, with a 12 volt solenoid , I am assuming the starter is a 6 volt Auto-Lite MAK 4053M 5K, I realize you can use a 12 volt battery with a 6 volt starter, but my main concern would be is the 6 volt choke solenoid. My plans would be to use a 6 volt battery and 6 volt bulbs in the running lights and use a 6 volt solenoid.
You will be limited in what you can power with a six volt system, and will find that even 6 volt bulbs and such are not getting easier to find. If you had an intact 6v system and no accessories to power, I would leave it. But since you don’t, and already have some 12 volt components, I would probably change it over. I assume there is no generator involved.