I'm battling the same issue. So you are saying the head unit needs a different power source more directly related to a direct power source same as the engines? That would be why the noice is less if the switch is set on dual while the engine is running.
Would an added battery and direct wiring do the trick? In lamens terms, what is the best route to wire this up so I can get rid of my noise too?
When I was a child, I used to talk as a child, think as a child, reason as a child; when I became a man, I put aside childish things.
1 Corinthians Chapter 13 - 11