pardon me for bringing up the obvious
...but many (all?) pumps vibrate a bit.
The vibration is not typically audible, but you can feel it if you touch/hold a running pump.
If you allow this vibration to be transmitted to your case - and if your case has lightweight panels (most of 'em do), then some of the vibration can turn into sound.
Try isolating your pump from your case to see if you have this problem.
If you're using a piece of mouse-mat (neoprene foam) that may not be enough isolation. Try picking the pump up in your hand for a moment to see if the noise stops.
If this is your problem, changing pumps won't fix it (unless the Quiet One doesn't vibrate at all - haven't tried one of those).
Try softer foam and/or add something to your case panels to make 'em less likely to vibrate (actually, you're just moving their resonant frequency out of the audible range). There are automotive products "designed to reduce road noise" that mostly all work for this - or you can be creative and use contact adhesive to apply something similar.
Again, apologies if you've been through all this already.
Bob