The Guitar Hero DLC is compatible with each game. I bought DLC on Band Hero and it worked on GH5 and Warriors of Rock. In my Wii's game data, it appears as World Tour DLC, and I don't even own that game.
Besides, it's an issue with installing the wad. I have the same problem and have not yet...
although i ended up accidentally changing my nand with no way of going back bc i didn't know you needed a gamecube controller to restore it (i have a wii minus/1.1, which doesn't have gamecube controller support)
and if i find the sd card i have my NAND backed up on, i can not only restore the NAND if i solder the right part in, but i can also put my NAND on dolphin, then i can play dolphin online, like PMEX Remix or MKWii Riibalanced