Ah yes, I like both of your ideas and yes, the HiFi's power button is a standby.
Hacking a molex cable into a relay sounds like a good plan, just need to test that standby button.
The problem with cutting power off completely is that when the HiFi powers on again it doesn't default into the Aux but instead the untuned FM radio.....
I'm not opposed to purchasing new audio gear if it gets me what i want