Hey Chino, thanks for your response. By plugging in the front panel audio header from a different case (NZXT), which resulted in the same noise, I felt I could safely rule out the case as the culprit. Especially since the previous motherboard I had installed in the case, an Asus Z170 Pro Gaming, had no problems with the front panel.

Admittedly the fact that all three of us use Fractal Design cases seems a bit suspicious. But in the thread I linked in the first post there is a user with the same case as me who is not experiencing any problems and all three of us are using Maximus VIII boards as well. I've spent today trying to isolate the problem and I'm leaning towards the board.

All that's left for me to try is to connect the header to the mobo of another working computer and see if the sound persists. Would you agree a silent result rules out the case/cable as the culprit? I'll leave any updates here in any case. More suggestions are always welcome!

EDIT:

I've just now quickly run another test, by plugging the HD Audio header into my roommate's MSI motherboard. It works fine with his board, no squealing. Should I conclude that I was simply unlucky with my board? Or could the case (rather the way the board sits in the case) still be the culprit? Looking forward to your opinions.

This happens to me on Cooler Master CM690 II advanced case as well as my brand new Corsair Obsidian 450D. Tried running the the front jack connector away from all power cables too nothing helps. Really annoying. If I switch to the mic port and make it a headhpone port the white noise high pitched sound is gone.

I have no problems with front panel. My case is Cooler Master CM 690 III.
Could be a problem with cable, connectors and/or drivers in your OS.

Hey MrDartay — I'm the OP of the thread you linked. I was able to solve the problem by reinstalling the drivers, but unfortunately it only worked temporarily. For the past few months I've gotten by with a barely audible white noise on my headphones, but now it's back. Just the other day I booted up to find my speakers making a loud hissing noise. They were not set as the default device, so I set the speakers as default, which made a loud pop before the speakers started working normally. Then I set the headphones as the default device again, and now my headphones are making that same annoying high-pitched whistling sound. I'll try reinstalling the drivers again tonight and see how it goes.

Edit:
Just finished reinstalling the audio drivers again. The hissing stopped when the computer rebooted the first time after uninstalling the drivers. Before it installed the drivers again, the headphones were quiet, but when a notification sound played there was some noticeable noise behind the system sound. After rebooting the second time with the new drivers installed and getting the front and rear audio devices separated again, everything is fine, and system sounds are nice and clean.

I have no idea what triggers the audio to start screwing up. At first I was just noticing that while watching YouTube videos it always sounded like my headphones were blown, as there was always a sort of distortion behind certain peoples' voices. Then in World of Warcraft I started hearing a crazy amount of reverb behind all the NPC dialog. Then suddenly the whistle was back... I didn't make any significant system changes recently other than installing some games and the curse client. For a while I know I was running an overclock that wasn't quite stable enough, but that should not be the case now, as I dialed it down to 4.5 Ghz without cutting back on the voltage I was using for 4.6 a few months ago when I had the system crash in the middle of doing a render in Maya.