Audio has static across distributions with and without using a USB adapter

I have a desktop machine with the following audio ailment:

• When playing audio over the headphone jacks (green, either front or back), the speakers are rather noisy/staticky.
• When doing the same through a USB adapter (I've tried two different ones), the problem is lessened somewhat, but I still have to unplug my speakers when not actively playing something since the static is still audible. That this doesn't fix the problem seems absolutely nuts to me!

Here's what I have tried:

• Tested the speakers on a different machine. They work well there, and multiple different known-good speakers have the same issue on the troublesome machine.
• Tested the system across multiple OS's (Mint, Arch, Qubes) and revisited it over multiple kernel releases with no change.
• Verified that I'm on the most recent BIOS, and have even reinstalled it in debugging efforts.

Unfortunately I have not been able to test audio output with my graphics card over HDMI due to not owning a suitable monitor (all DVI or VGA). The motherboard is a GA-F2A88XM-D3H revision 3.0, and I see that revision 3.1 boasts "Audio Noise Guard", so I'd bet that this is a common problem (though I have yet to come across someone else with it).

Do any of you have suggestions or workarounds? I'd rather not buy a new motherboard, but it seems like that would be the next step.