Acually i didn't finish reading your post...you are using a factory headunit, correct? What brand amplifier are you using? Running high level (speaker level) directly into the amplifier for signal is always asking for problems. The manufacturers usually cut corners and put in cheap line output converters in them. In addition they do not like "high power" factory headunits. If your factory ford radio has the amplfier behind the glove box, this maybe too much power for the line output converter to handle. I know the factory radio sucks, but the premium sound systems have more power then most cars come equipped with. Try going to a local audio shop and picking up a quality, external line output converter and this may fix your problem. That and a good ground as i mentioned in my above post should fix your problem.
Cheers
rimmie