All right I realize it's been like a month and a half, and my solution doesn't feel the most elegant, but I would rather put this out there for anyone it might help.

I did manage to finally fix my sound issue by upgrading my current kernel (Slackware 14.0 ships with 3.1.x) in order to get a newer version of alsa. Like I said, it felt like overkill, but I've been working on this for months, and absolutly nothing else helped (except running my CPU at a high load, like when I was compiling software). I used the instructions from here, but replaced kernel 3.8.1 with 3.10.17 (so I used https://www.kernel.org/pub/linux/ker....10.17.tar.bz2 to download the kernel source and http://slackware.mirrors.tds.net/pub...ge-3.10.17.x64 for the config file).

Hopefully this manages to help someone else or, ideally, no one else runs into this issue themselves.

Good luck, and thanks to everyone who tried to help me out.