Gysbreght
The BFO's for a northern route would be about 78 Hz greater than the logged BFO's in level flight. To obtain the logged BFO's on the northern route the aircraft would have had to climb at 3360 feet per minute during the 343 minutes of flight remaining after the first 'ping' at 18:25 UTC. That is 1,152,480 feet.
Come on, I do not understand the whole mathematical stuff involved but the handshakes are just that, one transmission for a very short time, giving BTO data which locate the arc and BFO data which tell something about the speed from or to the sattelite. This speed is a function of sattelite movement to the north or south, aircraft altitude, track, horizontal speed and vertical speed. We have an equation with one known (sattelite movement) and 4 unknowns (aircraft data).
Only during the short time of those few handshakes about 1 hour apart from each other the BFO data have to be fullfilled, not for the whole time of the flight. The flight could do circles in between, as long as it reaches the corresponding BTO arc at the next handshake and fullfills the respective BFO data. On what heading, speed and altitude that would take place or if the aircraft is climbing or descending at that very moment is not shown by the data.
Your computation assumes again a given track and a given speed and the computed vertical speed not only for the respective time of the handshake, but over the complete flight. It is the assumption that it was flown on autopilot with one fixed final target until end of the flight.