think about it, you alt puts out how many amps? lets say its 100amps, the car uses 70-80amps with everything on. the saz1500 can draw 160amps so that leaves you with 130amps unaccounted for. granted the amp isnt doing max power... ever. but it still leaves you with about 60amps unaccounted for. so, no. the big 3 will not be the perfect answer. its something that will help and is very needed if you ground the amp in the back. you would do just fine upgrading the front battery and adding a moderate sized one in the back... but thats more weight. you could get a HO alt but its a little overkill and itll bog down your engine just as much, if not more, as the extra weight in the car. although it should be more reliable because the alt wont be working at full output all day long trying to keep up with the current demand.
start with the big 3 and upgraded front battery and see how that works for you.