Are you sure that fan noise is from the PSU?

There is a small fan next to the motherboard, it is supposed to pass air over the heatsink in front of it, but apparently it does almost nothing to help.

So you can actually remove that fan.
Also because it is mounted to a short plank of frame, it can vibrate a lot!
I think this sound is actually that fan vibrating that frame.
Remove the fan or unplug it and see if the sound goes away.