oldoberon,
I meant that if there is any spectral information recorded, you could get a Doppler shift from the received frequency at the satellite.
Unless the aircraft is flying on a track perpendicular to the satellite, like the red arc, it has an approach or recession velocity, and so could give a link between direction and speed, depending on whether the signal from the aircraft was sufficiently narrow and consistent in frequency to measure the shift hour by hour, and the satellite measures frequency sufficiently precisely.
I suspect it doesn't.
I agree with you that the Inmarsat-3 over the Indian Ocean has a single beam that offers coverage out to 82 degrees away from the point beneath the satellite measured around the Earth.