Not a lot of "messing around" to convert to 12V. I recommend you convert. Bulbs, one voltage reducer, one alternator, one coil, one ballast resistor. Probably about the same price or less than a new 6V battery. 12V is WAY less trouble finding parts in the future and a long list of advantages.
The owner told you it was all original. You could look and determine that before purchase. He said it was converted. Many folks don't know how to do that. No crime in that, you may not know how either. So there is nothing to be frustrated about. Refurbishing old vehicles has some frustration now and then. It's fun and fulfilling most of the time. If this frustrates you, with all the help available here, you need to take up another hobby. Gather your Engineering experience and confidence, this is small potatoes. Many older trucks have a different/upgraded motor. That is no big deal. That can be a good thing.
1. Can we help you analyze this new truck's electrical before you do anything more? You will need a multimeter or voltmeter. Later we will help you wire it 6V or 12V. It all depends on if you have time and can respond with results.
2. Does it run?
3. You say you had "starting electrical issues". What exactly does that mean?
4. I realize, so far, you are not asking for help. Sometimes we rush in too fast. A rant is just fine but belongs in the spoon/rants

. We ourselves have morphed it to electrical. There is no electrical question pending.