Great stuff, Hugenous! Just added you as a 3rd blog worth keeping up with.

To answer the quiz question:
A function is even if f(-t) = f(t), or symmetric about the y-axis.
A function is odd if f(-t) = -f(t), or symmetric about the x-axis.
With 1 diode at the output, harmonics were from periodicity of the input signal convolved with contributions from the Taylor expansion of the exponential. If we think about the output with respect to the input sine wave, then the output is neither odd nor even so all harmonics show up (spectrum analyzer uses zero-crossing as frame of reference?).
But with 2 diodes, the output signal becomes symmetric about the x-axis (or an odd f'n), so the even harmonics no longer contribute to the output signal. The residual even harmonics probably stem from the difference in reverse leakage current between the two diodes.