Use "Play Soundtrack" trigger, set Category to "Music" and Soundtrack ID to "Music_Silence". Make it default.
This will make the music channel mute, it works better than the literal "mute channel" trigger.
Then, play your custom sound, and assign it to the "Music" group. Now it will play, with the benefit that the player can adjust the volume in the options menu.
On a side note, if anyone has trouble figuring out how to make music loop: On the Sound entry, be sure to set the Loop Count to "-1", and on the Soundtrack entry, be sure the "Continuous" flag is set. (it's on by default if you create a new entry, but if you duplicated an existing one, this may not be the case)