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The smaller in-camera JPEGs are downsampled from the RAW using a method Nikon will likely not disclose, but rest assured they are not "throwing away every nth pixel".
I wanted to also feel like I was at least getting better signal:noise when I shot Medium or Small JPEGs and it sounds like I am.
So I'm less than convinced that we can further improve SNR of highly processed images by averaging, since the noise components of adjacent pixels would no longer be independent of each other.