I was able to get the soundtrack of Quake 1's base game playing by putting the music files in the game's readily available, yet empty "MUSIC" folder, and changing the name of "_winmm.dll" to "winmm.dll", however I couldn't get the soundtracks of the mission packs playing in GLQuake no matter what I tried.
I have absolutely nothing against unofficial source ports like Quakespasm, but is there any possibility for the mission packs to have music in GLQuake or would another source port be required?