If the generator has enough overhead (extra voltage ability, and it's determined by the number of windings in the armature) to make 12 volts at a current that is useable, then you may be able to just swap the 6 volt regulator with one of the 12 volt flavors. I've done this on a couple of old forklift trucks with success).
If the generator will not make 12 volts with a load on it when the engine is running at operating speed, well, you're kinda stuck with changing the generator.
To reverse the polarity of the generator, you should be able to "Polarize" it using the same methods you'll find in the "Old" car manuals that cover cars as late as the 60s. You should also find test proceedures for the generator in the same manual(s).
The reason for polarizing the generator before placing it in service is to make sure the "residual" magnetic field is going the correct way for the polarity of power you want to get out. What could happen is the residual field will allow the generator to start making power of the wrong polarity BEFORE the regulator has a chance to apply the correct polarity power to the field winding, and when the main contacts close (and sometime weld themselves shut) your electrical system grunts just before the smoke leaks out of the parts that are made out of "Costlyum" or "Unobtainium" (saw a guy loose the labor of love 55 Chevy he had just rewired because of an un-polarized generator).