Alex,
I had the problem in reverse where the clicks where very noticeable with the factory nano as mounted on the Raduino.?
After? I changed the nano for a cheap eBay one, the clicks went away (as well as the audio tones I had).
This seems to indicate large variations in values of some components leading to part-to-parts variations.
Maybe better luck with the next one unfortunately.
All the best,
73, John (VK2ETA)