What you need to do is take that big new LED display and use it as an actual computer monitor, rather than as a stand alone presentation display.
From what you describe (and without a make and model number, as well as your partial description of the situation it is hard to do more than guess) the LED display has it's own operating system, and it's own media players. You are playing the music with the media players that are installed on that operating system, and they don't offer a visualization option like you would find with VLC or Windows Media Player, or Winamp, etc.
Now. If you were to connect these big LED displays to a computer and use them as a monitor, then you could indeed drag a player window onto them (or just clone the display, and make both the main computer monitor AND the big LED display show the same thing) and have a visualization display that way.
Otherwise you need to find out what OS is running on those TVs, and work out what software you can install.
Unless of course, there are details you are leaving out that would change the entire aspect of the question itself.
EDIT so, since you can't connect the screen as a monitor, and it only displays the output generated by the LED Vision software, and that software will accept a video... you can use any music player that you like that generates visualizations, make it display full screen, play the music you want, use software like CamStudio to make a video of the desktop (thus getting the visualization and music synced together) and play THAT video through the LED Vision software.
You wouldn't be able to do it live per se... meaning you couldn't just start playing random tunes at the time of display, but you could make a bunch of videos ahead of time and play those randomly.