I found an alternative winmm.dll wrapper based on this guide and the Vanilla Restoration Patch. I've used it on Quake I and it works pretty well and music seems to loop whereas the one shipped with the GOG version doesn't, although the music does restart when changing resolutions in WinQuake. How I got music back in Quake without a source port:

1. Download ayuanx's ogg-winmm wrapper here, there extract its contents to your Quake installation folder: https://github.com/ayuanx/ogg-winmm/releases.

2. Rip the game music using a) a combination of IsoBuster to rip the lossless audio + oggdropXpd to convert the files into .ogg files however you like based on instructions from this post or b) use CueToOgg.

3. Rename the converted tracks for Scourge of Armagon from track02.ogg through track07.ogg as track12.ogg through track19.ogg, then rename the Dissolution of Eternity tracks as track20.ogg through track27.ogg.

4. Move all of the music files and put them into the "MUSIC" folder. If one doesn't already exist, make this folder and name it "MUSIC". You should have 26 *.ogg files as shown in the attached screenshot.

5. Make a music.cfg file in Scourge of Armagon (hipnotic) folder and add the following with a text editor (e.g. Notepad)... and make another with the following for Dissolution of Eternity (rogue)... 6. Create or edit an existing autoexec.cfg and add the following line: Now try launching the game, ayuanx's ogg-winmm wrapper should be able to play the music right from the MUSIC folder.