When I was 19, my friends and I were building cars that would lift both front wheels off the ground coming off the line, and would travel at speeds well beyond the design of the chassis, the tires we were using, and the highway system. At least, the only thing you are endangering is your hearing. We were endangering ourselves and everyone else on the highway.

I believe that it would be worth your while to start at the amp with a voltmeter. The battery should pull your sound system for several minutes at least, regardless of the charging system. If you don't diagnose the problem, you may find that you still have the problem after your alterations.