But with that in mind, since I'm not finding much else to go with, let me point to a couple of Ubuntu articles concerning Beats Audio and alsa configurations. I don't know if the hda-jack-retask app is available in the AUR, but it looks like the source (by David Henningsson) is available in links on these pages.
I've already tried that; it doesn't seem to have worked for me yet. The last time I used it, it showed a different driver and different pin numbers. Right now it's giving me segfaults when I try to run it after a stream of lines like this:
(hda-jack-retask:6028): Gtk-CRITICAL **: gtk_combo_box_text_insert: assertion 'text != NULL' failed
The AMD graphics drivers should not have any affect on the internal sound card. From your first post the audio card is supported by intel audio. Digging through the thread a little, I noticed you tried building a driver for the 3.0 kernel. Assuming you are, in fact, using Arch generic then the 3.0 kernel drivers will not work. Arch has not been on the 3.0 kernel for some time and drivers for older kernels usually do not work on newer kernels. I would suggest using a pure installation not from a script.
Concerning AMD GPU drivers in general, on ARCH the only officially supported drivers are the opensource drivers. Please refer to this page for installation instructions: https://wiki.archlinux.org/index.php/AMDGPU
I'm trying the Intel drivers and AMD drivers now; I've gone on an installing spree.