To add more detail to my situation for those who may be able to help with this problem.
I've now tried Antergos and Fedora Live environments, and also booting into my Windows partition (stupid Matlab for school...) and I've had issues in all of them. This warrants some more information about my previous operating systems and how they interacted.
Before dual-booting Manjaro I was using Fedora 20 and Windows. Audio worked just fine at the time. I had learned quite a bit while using Fedora and felt a little more confident to move to a system based on Arch. I then install Manjaro and the issues began. Audio becomes as described in my post that I link to in my last post here. I worked through trying different things for PulseAudio and Gnome, I then worked through switching to XFCE and removing Pulse all together in order to see if that was the problem (it wasn't). I then tried messing with ALSA (which to be fair I probably haven't exhausted the possibilities) but I'm finding that alsamixer is saying sound is being output to correct interfaces, those interfaces aren't muted, etc. I know it is in fact doing that because audio will play for a few minutes through the speakers and then all of a sudden turn off (headphones still work when plugged in). I then went to a friend's house last night to LAN and I booted up Windows for the first time in a while. I tried my Windows partition and here's where I and @erik are definitely having the same problem with the same hardware. My Windows partition will begin playing a video for instance, it will play for a little bit and then mute like within linux, but this time if I move to another buffered area of the video, it will reset and play audio for another minute or so. I had never had these issues within Windows before with Fedora, so I figured I'd try a live environment of Antergos, to see if it was a Manjaro thing (Arch base being equal), and Fedora, to see if that still worked (spoiler, it didn't).
So here we are, a week ago I had audio playing through my speakers, installed Manjaro and have had issues since. I don't know if there is something that Manjaro updated micro-code on the processor, or made some persistent change to the audio, but something happened that has affected audio across distributions and completely different OSes.