I doubt a "big" alternator will fix your dimming issues.
There'll still be too much output resistance in the alternator and too much time lag in its load regulation for it to be effective against large transient loads like bass hits.
There's also too much resistance and inductance in the wiring, even low-AWG stuff.
You need to store energy in a very low-impedance source at the point of the load (i.e. a low ESR capacitor.) It's the same principle PCB designers use when they put bypass capacitors at the power pins of power-hungry processors: it helps reduce the effects of inductance on the board and in the power supply wiring and ensures the processor gets decently clean power as transient demands vary.
In addition to low-ESR caps a second, auxiliary battery, placed very near the point of load makes a good low-impedance source for stuff like amps. It can be charged by the car's alternator through the use of a marine battery isolator.