When we did our conversions from 6 to 12 V, most rodders would change the generator, starter, and voltage regulator, I remember asking the friendly old guy that ran the auto electric shop why not just use the 12 v regulator. His answer was that it could work but the 6V generator doesn't have as many windings in the field coils. and would require a higher rpm to put out the same voltage as the 12V design. So, it doesn't mean that it wouldn't work, but that you would have to turn it faster.
He was also the guy that told me to save my money and keep the 6V starter, it is wound with heavier wire and would work just fine. I never had any problems.
I have a dirt simple 12V plug_in charger that is still working for me (20 + years ) and I even use it to jump start my old Bob Cat loader. I even ran over it once, blush, and it still works.
Bob