However! After a ton of google searching and realizing while attempting to listen to a binaural video, I was able to figure out that the left and right audio channels were being mixed into mono. From there, I found out that it's because the Beats program sets up SRS effects in the registry that it doesn't allow an interface to change. For some unknown reason, channel mixing is among those effects (eew).
I found the registry alterations necessary to turn the horrible channel mixing and volume leveling off... and still reap the benefits of having a bit of a bass boost per my settings in the equalizer. So thankfully that nightmare of frustration is over and now I don't have to put up with the default Windows drivers any longer.
Thanks for responding! It did turn out it wasn't actually drivers at all, but sadly wasn't as simple as just swapping programs. Shame on HP for making things so difficult and intentionally setting audio to sound like it's mono!