it does not seem logical that letting a camera perform a DX crop would have less noise than doing it in post
I thought the same thing until I saw the numbers and worked it through.
As a preview, try to visualize this. We have two curves and the distance between them vertically is in the proportion that we would expect; for example 1.5:1 But the distance horizontally between the curves does *not* match our naive expectation. That would only be true if they were straight lines starting at the origin with slopes in the 1.5:1 ratio.
More to follow. Other projects like my site update regarding charts is keeping me from getting this from my head and onto paper.