Your alternator operates at around 14v, usually 14.2-14.4. A fully charged battery has a voltage of 12.6.
So as long as the engine is running, the alternator is the power source. Batteries only come into play when
1) starting the engine
2) fractions of a second when the alternator is responding to a sudden increase in current demand (like high volume bass)
3) When the alternator s output is exceeded.
When the engine is running, the battery becomes a (small) load for the alternator to charge.
Condition #2 is likely the cause of your headlight dimming. The difference in the light output of the headlights is the difference between the alternator s ~14v and the battery s ~12.5v. I think it is important to recognize that some degree of headlight dimming at idle is to be expected with a 1000w+ amp. As long as it isn t enough to distract other drivers I wouldn t consider it a problem.
The 197A current draw you mentioned is not what you actually have going on. 197A would be min impedance, full volume 0db sine wave current draw. At FULL volume playing music you are likely in the 50-75A range -- maybe some bursts to 100-150, but on average, much lower. At low-moderate volume it's probably well below 50A.
If you truly want to solve the issue find a small capacitor (doesn t have to be high priced, a little $40 off brand 1F cap (or even 1/2F if you can find one) would do it) and install it on the power feed to the headlights.
A battery may help, but not necessarily for a good reason. With two batteries to charge, the running voltage of the alt will likely be reduced slightly, and with two batteries to support the sag in voltage it will likely be slightly higher.
Personally, I would just turn it down a couple clicks at idle -- obviously, that is the cheapest, most effective solution.