There is soo much over thinking in this. Makes my head hurt

If your car dies from running the stereo for a few minutes with the car off, it's 2 things
A **** battery or a massive system
Or your cranking up the volume with the car off

Get yourself a nice red top. It will have the reserves to take the hits from the amp. Your lights should never dim at idle at a light. Even with the system pounding.

I wanna take a video of my gauges and amp at idle. You would be amazed. 14.1-13.8