Yeah those are cool parts. They are buck gates and low/high MOSFETs and diode all packed into a package also do current sensing and each can handle 40 amps. So 5 phases and 5 of those means that GPU of yours can get up to 200 amps!
I think the only nitro+ with higher is the Strix which has 3555 each of which can handle 60 amps.
Since you opened the cooler and back plate I've seen whine getting better or worse by tightening or loosening the screws on the pack plate and heat sink/cooler assembly. More or less pressure might disrupt the harmonics of the oscillation therefore reduce the noise a bit.
Coil whine is almost always not a problem and does no damage to the components. Caps hissing must be taken seriously as it's warning that the cap is going to blow soon. No worries with coil whine.
If it was intact I wouldn't touch it but since you already opened the cooler and back plate up I would try tightening or loosing the back plate or cooler screws a very very small amount to see if it changes the whine. So small a change that does not change the proximity of the card/cooler to avoid imapcing the whole cooling process of course.
I just remembered something that's relative to the whine issue. You can try and see if this happens we can know this is a tool that might work in some cases to identify whether the noise user hears is a coil whine from GPU.
Only thing that has made my card whine is some 3D demos/tests that come with the GPU Caps Viewer by Geek3D. You can get the latest portable version from here and see if they make your card whine too. It'd be worth experimenting I guess.
If you like get the software and I'll check on my desktop later to see which demos it was.
Mine is quite audible in GeexLab demos OpenGL 4.0 Tessellation v3 v2 ad v1 in smaller window size.
If I maximise it it goes really silent or I'm not able to hear it anymore.
On the rest it's almost nothing or nothing at all.
Now that you mention it I'm not sure whether the whine is coming from GPU or PSU. I'd have to check closely later.
Edit: Noticed something else. Their previous version as soon as you closed the demo/test window GPU and VRAM clock would jump back to idle but with the new version you have to go to other tan in GPU Caps viewer or close it altogether.