Good day! It seems to me that the best option to reduce noise is to install drives with a lower rotational speed (5400) and a larger cache. Another aspect of noise reduction is replacing the fan with a more technologically advanced one, I prefer Noctua fans. But you showed an interesting experience of personal use, thanks!

the nas doesn't make the noise. that popcorn sound is all hard drive sounds. some drives will make a lot less noise. i have an older hgst and it makes popcorn sounds when its running too. i am too broke to update the drives so i decided to get a noctua fan because i have had good success with them and the fan header looks like it has a standard pin layout for the fan you might want to try wrapping the foam around the drive cage itself, especially on the parts that tend to vibrate and hit the inside of the metal case. that could reduce some noise. also using solid state drives will make the noise all but disappear.