Can I reduce the amount of noise created by metal shrinking after the fireplace is turned off?
There's not much from a practical standpoint that can be done. Obviously, as metal heats it expands and as it cools it shrinks again. The creaking primarily comes from seams in the firebox and the flue that move against one another as they cool at different rates.
Nothing will totally eradicate the problem other than possibly uninstalling the unit and reinstalling it with fused/welded seams to reduce the friction. It's impractical and even that would only reduce, not eliminate the noise. You might contact the manufacturer.