Make sure the gauge of your ground wire matches your power lead. You mention 1/0 coming from the engine bay and 4 gauge for the ground. Probably not an issue with your current amp as it's power requirements are lower, but if you move to something like the Taramps 3k, you will want at least 1/0 for power and ground, and you many want to consider a double run for both power and ground.
As for clip mentioned previously in the post, low/sagging voltage can drive an amplifier into clipping, especially when the system voltage drops significantly lower than the voltage it was tuned at. As an example, if you tuned your amp with the electrical system managing to maintain 13.8-14.1ish volts, but while playing the system your voltage drops to 12.4 or lower, the amp will almost certainly be driven into clipping. It has to do with the power supply voltage (a square wave supply in a class D amplifier for example) sagging lower than what the output side (an analog signal) of the amp is trying to deliver causing the peaks and valleys of the audio signal to "clip" looking like the tops and bottoms of the square wave rather than clean analog peaks and valleys.
So like Dafaseles and Anthony mentioned, moving to something like the Taramps (or any other 2500-3k RMS amplifier) you will want to prioritize a high output alternator as soon as your budget permits. Just try and remember - batteries and caps store power, your alternator is what actually generates power. You may be able to store up some power in the batteries, but your voltage will sag and you will exhaust them and have to turn everything down while they recover/recharge until you have the alternator(s) that can keep up.