Yeah so I'll clarify that for OP. The numbers I gave are for playing your stereo maxed out, for hours on end. If you listen to it like that with that wattage, you won't have any problems at all. There is still plenty of wiggle room in there.
If you listen to it for a few songs at high on full, once you turn it down, your alternator will be recharging your alternator at a rate greater than what you are using. Batteries are a storage bank, and with your second one, you probably have a good hour or two of playing a 1200w sub at full before it drains your battery with no alternator.
With that AGM battery, I'll bet yeah you're in that 3k-4K range (depending on the battery specs) where you wouldn't notice lights dimming until you start draining the voltage at a rate faster than what the alternator can recharge and for long enough to where it drops below 12v. With what you have and lets say 3K watts, it depends on the kind of music as to how much you are actually pulling, it's not constant. You would be recharging in between the bass hits, (it's not a steady, 100% draw). Rap is going to use more with all the bass. Rock, country, and just about anything else has less bass hit, and has a little more of a gap.
You can definitely go bigger than 1200W. Personally, I would feel comfortable with just under 1800-2Kw amp on that setup for rock music, and expect no problems. If you are driving at some time after you turn stereo down, and don't play it for more than an hour, you could go a little higher.
You can also turn down an amp, you don't need to set it for max now in case you know or think you might want a second or upgraded sub later.