For Dungeon Keeper, I'd like to shut the music off while I have something else running, but the in-game option seems to have no effect when playing the game (works just fine for the title screen). Is there a way to do so?

To be able to turn it down but not off would be even better.

Strange. I remember having no problems with that. How about an ini file?

I had this issue ages ago!

I contacted GOG support and they gave me help on how to turn it off, so I can't help you turn it down but I can help you turn it off.

"Please go to the game's directory (default: C:\GOG Games\Dungeon Keeper), open the "dosboxDK_single.conf" file in Notepad and change:
cls
Keeper.exe
to:
cls
MIXER CDAUDIO 1:1
Keeper.exe

This should disable the music."

From gog support.