My installer put some resistors (75k ohms?) on a wire to bring the voltage down, but can't remember which one. I think he said the signal wires leaving the unit (sub out) as these were supplying immediate signal to the sub during AVIC power up. My AVIC-Z1 still thumps the sub when the AVIC powers up but not all the time and not always very loud. He said he could make the noise much less with more resistors but it wouldn't power the sub.
I'm not sure switching to 5V would fix this. You could always go with a model 7805, 5V regulator, if you wanted to and see if that works. This regulator would put out some heat, tho.