The dimming is voltage drop due to the current draw. You could throw more batteries at it, but if it's not excessive, I probably wouldn't worry about it. The AMP I'm certain has a switching power supply in it, so as the voltage drops some, it will compensate to keep the power output fairly constant. Depending on how long you're keyed up, the alternator may not have a chance to react anyway. At an idle, I don't care if you have a 400a alt... there's not enough engine speed t make any appreciable power. Running down the road at 1500-2000 rpm, I'd bet that factory can hold it, or at least very close, if you're on for a few seconds.
But yeah, you might want to keep moving because if the FCC finds you... you're gonna be hurting. Although anymore I don't know if anybody even cares about HAM, shortwave, FRS and CB channels.