Just get jazz2+, run a level, and type '/np'. This will display the file you are listening to. Then go into your C://Games/Jazz2/ folder then search for the file there. It is openable in winamp if it is an *.s3m file, an *.it file, an *.xm file or an *.mod file. If anything else, you can't listen to it.
If you feel the need to, you can copy the files to any place where they are easier to find. (Like on your desktop, for example.)
Whenever I can, if I'm building a level I usually listen to the song the level uses while using JCS.
But I have a lot of patience, and while that might seem very tiring, for me it's not.