Our first step to improve the situation will be to protect the audio signal wires by shielding them with the screen of a coaxial cable.

Here, I have used the shielding of a short piece of video cable for this purpose. Cut the outer plastic insulator of the cable and remove it.

The wire I'm using here is double shielded: There's a braided shield and also a layer of aluminum foil. We are going to use both shielding components. The more the better ;)