Update:

Obviously there is some sort of power backfeed into the audio system, but darn if I can find it.

I decided to try an experiment today and used a set of Ground Loop Isolator RCA's to connect the 4 channel amp to the 2 channel amp.

The problem still occurs where I get a bunch of static / nasty noise, but only for a very split second and then I get music. I think I also now have alternator whine that I didn't have before, but I'm not positive - have to do an A/B test.

Not surprisingly, I found that the shields/pins of my tuner unit have no continuity amongst them. By contrast, the shield of all channels of my amplifier are connected. I believe that what has happened is that I have balanced inputs from the radio (which I knew) and that the amplifiers I chose that I thought supported balanced RCA's actually do not. My suspicion is that connecting the left and right shields is equivalent to connecting the left and right pins (since the radio provides balanced outputs) and is causing an issue. Using a GLI obviously isolates the shields and seems to eliminate the issue...

I'd be more than interested in anyones thoughts on whether or not what I indicated is a possible explanation...

Doug