You are in luck, the 370Z has a 150 amp alternator. You will be able to support the audio system however I highly recommend you get a better battery like an Oddysse or a Stinger thats designed to support a high powered audio system. Your stock battery may last a year if that. Most people over look these issues and wonder down the road why they have electrical problems with thier car.
I would recommend you go to a welding shop and get some 1/0 power cable. Welding cable is way cheaper than audio cable and its just as flexible but its pure copper. Then split it off to 4 gauge to each amp.
Your choices of components are very good, I really like MB Quarts but they are not as popular as they were 10 years ago but they are still as good as they used to be if not better. I would however recommend the 12W6V2 over the 12W7. I feel the W6 is a much better sounding sub. W7's sound heavy and are more of an SQL sub. The 12W6V2 will already pound your head into pulp in that size of a car.
Running this sub instead will save you a lot of dough. Its half of the price and you wont need that 1000 watt amp. The JL Audio 500/1v2 would be a perfect match and take less of a toll on your electrical system and wallet. Any more power than that is a waste and it your sub will last maybe a year before its cooked. Been there done that.
The HD series 4 channel amps are really the way to go. They are way more efficient, easier to install due to small size. You should look at the HD 900/5 amp. Its a beast of an amp for its minute size. I have one running in 3-channel mode at 500rms to the sub and 200 watts X 2 for the the front speakers.
I am running the rears off of the deck power for just a touch of rear fill. I feel the rear speakers make the music a bit more enveloping but most people dont bother with them. Its an old school trend that I have just never let go.
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