There ended up being 2 issues to solve in fixing the background noise issue.
1) I bought a ground loop noise isolator. Put this in line with he RCA audio cable, with ground lead connected to the cars battery ground.
Here's the noise isolator I bought: http://www.amazon.com/gp/product/B000K50HJE
2) The 12v to USB power adapter / converter I was using initially was a really cheap one that wasn't providing good power to the Raspberry Pi. I replaced this with a much better one.
Never use cheap USB power adapters. Here's the USB power adapter I bought: http://www.amazon.com/gp/product/B00VH8VHWO
After making these 2 changes to the system, the audio no longer has any hum or background noise.