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You only gave us the model of the amp so I will make an assumption that your 12" subs are the Sony XS-GTX120LW. First, they cannot hold 1200 watts a piece. They are meant to be powered with 350 watts RMS. They will hold 1200 watts peak. That means that 1200 watts for a few seconds will be ok. Past that and kiss them goodbye!
Next you indicated that bridged the amp. Since the subs are both 4 ohm single voice coils did you wire them in series or parallel?
It sounds to me like you wired them in parallel resulting in the amp seeing a 2 ohm load. The amp you referenced is only stable when bridged at 4 ohms.
Has the amp begun working again once it cooled down? If not you could have fried the outputs by having the resistance too low.
You should definately bridge them. Firstly, lay the 2 speakers face down next to each other. Note the connections +- +-. The first + will go to the amplifier. The next terminal(-) will be connected to the next speaker(+). Take the last(-) and connect to amplifier. Please note that your amplifier has a bridge section which is normally the first + and the last- on the two channels. Connect your woofers on the bridge.
IF THE RMS IS 800 THEN THAT IS THE MINIMUM YOU SHOULD RUN TO THEM. IF THE MAX IS OVER 1000 WATT, YOU SHOULD BRIDGE ONE SPEAKER TO EACH CHANNEL. YOU WILL PUSH THE MOST POWER TO THEM THAT WAY. MORE POWER = MORE BASS
The head unit may be rated at 200 watts but it cannot produce more than ~20 watts of real power per channel. There's no way that it can drive the high end speakers to a level that will be needed to compete with the subs on a 1000 watt amplifier.
That's not a 1000w amp. It's a 400 watt amp when loaded to it's lowest rated load. If you have one speaker per channel (the only safe load if you have single 4 ohm coil speakers), you're only getting 165 watts/speaker. It's probably distorted because you're driving it to clipping.