Hey, I don't know if you've figured this out or not yet but my guess is that your iPhone 4 with iOS6 isn't the problem. I bet it's your deck. If you can update the firmware on your deck, try that. Your deck might have been designed before iOS 6 was even a thought in Apple's mind. But there could be a firmware update that will make the deck work with iOS 6.
As for the iPhone 5, I found out the hard way that I can't run video (i.e. Netflix
and YouTube) from my iPhone 5 to my deck, which I had done tons of times with my iPhone 4 with iOS 6. And i was further butt hurt when i found out the lightning to 20-pin adapters that are out now don't transfer video. They only do audio. I remember seeing online somewhere that this guy got it to work with two or three different types of adapters. I didn't donit because its more work than I want to put in for something I rarely use anyway. Sorry I don't remember any specifics about it but if you google it enough you'll find it.