One more guess about Doppler...
If the AES has to compensate for Doppler, it have to do this from its own.
When AES is pinged by the sat, it could "deduce" the offset from the signal frequency it receives. But it can't do that when it initiates the transmission.
How to do that?
From a patch of data (one for each Inmarsat sat) included in the AES?
If those data are related for a theoretical position of the sat, the remaining offset which was used to compare north/south routes could come from the wobbling of the sat which appeared slowly with the sat aging, and not included (or not "includable") in the data patch.
In this case, it could explain the low values of the offset compared to the true relative speed of the sat and a/c.
Il also could explain why there is no negative values in the published chart: the sat is at every time of the flight north of its theoretical position above equator.
Just an idea...