I figured out the problem. Both the primary Kaiserreich mod and this mod are trying to modify the main game's music folder. This causes a conflict, and the main game uses the files in the primary mod's folder rather than this one. There is a way to make it work until the primary mod and this one become compatible if you feel comfortable editing files. You will need to make an extremely minor edit to the primary mod's files. Navigate to the folder where the Kaiserreich mod is located. "C:\Program Files (x86)\Steam\steamapps\workshop\content\394360\809903394" is where mine is located, but it could be different for you if you installed Steam in a different directory. Double click KR (you'll need a program to unzip compressed files, I personally use WinRAR), and locate the folder named "music." Simply rename that folder. I personally just put an underscore in front of it. It should now appear as "_music" or whatever you chose to rename it. Now the game will only see this mod's music folder, and your music should work just fine. PLEASE NOTE: Before editing anything, I recommend making a backup of whatever you're going to change.

Edit: And this is now obsolete thanks to the quick work of the mod author. Thanks again Zarasophos!