About the "circle path": I am afraid it is the result of oversimplification of the sat and the airplane relative trajectories.
Why using a constant speed for the sat? Inmarsat 3F1 data are available.
In my very simple model, I don't use spherical coordinates but Lat, Long and Altitude, because it is easier (for me) to "see" the data. It is not very accurate because "my" Earth is spherical, but just for "see" what can be deduced from the "faint" known data, I think it is enough.
I suspect the circling trajectory obtained by Byan C is from not taking in consideration the fact that all airplanes flying along a "straight" line are, in fact, flying on a circle around the Earth. If the simplification include flying in a (flat) plane, the only way to follow the BFO values is to "curb" the trajectory in the (flat) plane...