JakartaDean,
I have always been sceptical that the logs would contain detailed enough data to estimate speed. Why would a desperate-for-storage-space engineer add logs for such extraneous information? (If she did, hats off as it may have made a difference to this investigation.)
That was my first thought too. But on second thought the single downlink sat -> ground station probably needs as much resources as one link between a/c and sat. To communicate with the a/c the sat has to "illuminate" the whole hemisphere to be receivable by a tiny a/c antenna. In contrast to that the downlink to the ground station can be one concentrated beam and the antenna on the ground can be huge.
Thus the resources spend for the one beamed downlink to the ground station are negligible in comparison to the thousands of unbeamed links to the a/c and ships. So why not use the "cheap" bandwith in the downlink to relay all data available to the ground.
BTW: Newer Aero-C Terminals have automatic doppler comensation.
Aero-C - Products - Aero - - Thrane & Thrane
Maybe older terminals required assistance from the satellite for that compensation, which would explain, why the sat "knows" the speed of the terminal.