I ran Windows 7 for a short while a long time ago on this PC, but I can't remember if I had that issue back then - I also wasn't running intensive applications like Battlefield 4 back then, either, which might be a contributing factor to this issue.
I went ahead and uninstalled the audio drivers, at which point my speakers were no longer recognized and it switched over to HDMI audio. Windows doesn't seem to be able to find the drivers on its own, so I reinstalled the official 6.0.101.1040 Creative driver from Gigabyte's website.
Also, if it's useful, I did an absolutely clean install of Windows 10 - hard disk wipe, then install from ISO
Thanks again for the help!