You can download specific DLCs but I’m not entirely sure they’ll be useable. It’s worth a try. Here’s how you do it:

Open a web browser and type in steam://open/console and it should open the Steam console inside of Steam itself. Type download_depot <game_id> <depot number> for Rocksmith the game id is 205190 and you can look up the specific DLC you want on steamdb

So for example, the Pearl Jam Song Pack could be downloaded using download_depot 205190 222139

Rocksmith’s DLC SteamDB page: https://steamdb.info/app/205190/dlc/

If this DLC has been disabled as you said, this might not work, or you might need to make sure that Steam doesn’t try to update the game (which would disable the DLC again). You can do that by browsing to ~/.steam/steam/steamapps/ (assuming you’re on Linux, or just wherever your “steamapps” folder is on your PC) and find the file called appmanifest_205190.acf and set it to read only. That should prevent Steam from modifying any changes you’ve made to the game. Just remember to set it back to writable if you want to update the game again.

The game might not recognize the DLC as I said, but you should be able to access the files anyway if that’s all you wanted. They’ll be in ../steamapps/downloading at least until the download is complete, then it should try to apply the DLC to the game, which might cause the files to get deleted. I’m not entirely sure about that.