New system: problems and solutions?

[Rumblebug]

First off, I'll put up pictures right at the end of this post.

I finally got around to hooking up a system in our Beetle, and ran into some issues.
First, the car is a 2001 tdi, non-Monsoon system. My wife likes the way the stock radio integrates into the dash curves, and didn't want to lose the functionality of the 6-disc changer, so I was going to use a line out converter to run to a 4-channel amp, and had a powered bazooka tube to hook up as well.
Well, the system worked fine when the car was set on acc., but as soon as you turned the engine one, the radio would stop putting out a signal.
We (myself and 2 very good installers from Ultimate Electronics) messed with it for 3 hours, and tried different converters, and couldn't get it to work. So finally I picked up a Pioneer head unit......which ended up being too deep to fit in the car! The unit itself was ok, but with the rca's out the back, it would hit the dash support before it was fully in.
So, returned the Pioneer unit and picked up a Kenwood. FINALLY! Everything works. The sound stage is amazing! I love the way it sounds, even though we're not using high-end speakers.

Ok, so the setup is a Kenwood head unit, 4 Blaupunkts in the dash, Blaupunkt tweeters in the stock location, all run off of a Phoenix Gold Octane R 4-channel amp.
We disconnected the front OEM speakers, and left the rears connected, just running off the head unit itself. In the trunk is a Bazooka powered bass tube.