I had this problem a while ago, before I bought my new TV.
I used an old 360 component cable with the red, white and yellow connectors, this cable doesn't have the notch that stops you connecting a HDMI cable into the back of the 360.
I connected the component red and white cables to a triangular connector with a jack on the end--one that would fit into a head phones socket.
Then I used a 3.5mm Stereo Jack Female to Female Adapter to connect to the triangular connector to a line in source(back of my amp) via an extension cable.
I still used a HDMI as well, to get the picture.
I'm sorry if that sounds a little odd, I found it rather awkward to type, a picture would have been a lot better, but I don't have it set up this way any more.