I was finally able to get sound working, thanks to the bugreport here: https://bugtrack.alsa-project.org/alsa-bug/view.php?id=3104

What I did was get the patch_realtek.c from the bugreport, put it in alsa-kernel/pci/hda, and then re-build the driver (plus I re-built the lib, but probably not necessary). I wasn't able to rmmod snd-hda-intel after the build finished, so I restarted the computer, and then it just worked.

Unfortunately, the headphone jack is not working. The sound is only slightly, if at all, muted from the speakers when the headphones are plugged in.