Interesting. You also said that going from player to tuner and back again did not change the static.

The fact that you cannot control the volume of the static (and that it tends to sound like it's at the full amplifier volume) means that the problem is somewhere after the DSP stage. Meaning it still could theoretically be the car's amplifier, and the reason it resets with a reboot is because of the amp remote line resetting like I said.

Question: Does the static have a "digital" kind of quality to the noise, or does it sound like analog amplifier static? Not sure how to describe the difference, but I guess digital noise might have some kind of a pitch or buzz component to it, whereas analog static would just be pure white noise static, like a radio tuned to a nonexistent station.