Back in the 1940s and 1950s, ham radio operators with mobile equipment had to deal with the same issue with a vacuum tube transmitter. Chrysler products had higher output generators than cars from other manufacturers, so many ham radio operators used Chryslers. In many makes, a truck generator with a higher amperage output was used. For transmitters requiring a lot of power, a dynamotor was often used. One advantage of the 6 volt systems used in cars through the early to mid 1950s was that the wiring was a thicker gage and could carry more current than the wiring on the later 12 volt systems.
If you are intent on blowing out your eardrums with a high powered system, I think that deep charge boat battery to power the system is the way to go. It would be completely independent of your car’s electrical system.