If for whatever reason I
sudo stop lightdm running on mint and just use a simple xinit session with mutter, is there some way I can get sound to work? Whenever I do that, it seems there's no sound.
Check to make sure your applications are using alsa output as opposed to pulseaudio or esd (Or start those daemons yourself). Also make sure your mixer is unmuted with alsamixer.
I was able to fix this issue on Lubuntu 16.04 by installing
sudo apt-get install pulseaudio