Speed of sound,
I accept however that the final two pings being the same distance from the satellite would strongly suggest a stationary aircraft and more coincident arcs than that would suggest the aircraft is on land and not in the process of sinking or drifting and therefore likely to be on the 'northern arc'. Those are the only conditions that I see the prior pings being of any help to the search.
You're right - to fly equidistant from the satellite would require a non-great circle along the red arc. If the ACARS was powered off, the alleged miscreants wouldn't think they needed to worry about that, and would it even enter their heads what Inmarsat logged about data signals for Rolls Royce, and where their satellites were located?
If there are prior distance measurements, then they will help. They'll give a time to some unknown point on the arc, and thus constrain possible paths between points on the different arcs.
If the Inmarsat signal has a frequency measured in fine channels, which it probably doesn't, and better a change in frequency from signal to signal, since the properties of the transmitter aren't known, that might even add a point measurement of line-of-sight speed which would help improve the possible paths it could have taken.