When you limit the sweep to 20 kHz there is no data at the harmonic frequencies above 10 kHz for the 2nd harmonic, 6.67 kHz for the 3rd etc.
Percentage distortion at a frequency is the level of the harmonic as a percentage (i.e. divided by) by the level of the fundamental at the chosen frequency. Traditionally the level of the fundamental at the frequency of interest is used, so the level at 1 kHz when looking at the 1 kHz distortion levels. Temme's argument is that it is not sensible to use that frequency for the harmonics when the fundamental where the harmonic arises is different in level. For example, if the fundamental at 2 kHz is 10 dB higher that means all 2 kHz content for the system gets 10 dB more gain from the linear response than at 1 kHz, including any harmonics that fall at 2 kHz. Continuing to use 1 kHz as the reference level for the 2nd harmonic, for example, would then mean the 2nd harmonic would be reported as 10 dB higher than it really is, since 10 dB of that 2 kHz harmonic's level comes from the system's linear gain. That 10 dB isn't non-linear distortion. The opposite also applies, if the level of the fundamental at 2 kHz is 10 dB lower then using the 1 kHz level as reference would mean the 2nd harmonic level being shown 10 dB lower than it really is, since it has been reduced by 10 dB by the linear gain of the system at 2 kHz. Using the harmonic frequency as reference fixes that problem. When using the harmonic frequency as reference you are seeing very high levels for harmonics which are occurring beyond the point the linear response has rolled off, so the fundamental level is very low. What confounds that situation is the noise floor of sweep measurements, which rises with frequency. Your original plot shows that the harmonic levels have themselves fallen into the measurement's noise floor, so you really shouldn't be paying any attention to the reported levels there.
An alternative for your case, where the linear response is smooth if not flat, is to use the RTA, which has far lower noise floor, shows harmonics at the frequencies they occur and doesn't use the harmonic frequency as the reference.