Something that immediately hit me when I opened the game is that the music sounds not at all the way it's supposed to. If I open the MID files from the ALL folder in Winamp, they sound exactly as they should, but for whatever reason, they are of worse quality in-game. Is there any way to fix this?

Ok, I have found the solution... you need to open the pause menu with CTRL+F5, then Return to Launcher, then Settings > Audio, and in there, change the preferred device to Windows MIDI.

GOG sets the game up to use adlib sound by default. While this may not be how you remember the game sounding, it's not "wrong" per se. There is no "correct" audio device for a game using a MIDI soundtrack.