Hyperveloce
I have tested this for great circles between waypoints (LNAV mode), between BEBIM (and a shifted version to the east) toward 3 destinations: the south pole, the Wilkins airport and NOBEY
I am a retired airline pilot rather than a boffin. It looks to me from the data published that if LNAV is used it is likely that Wilkins (YWKS) was the "destination" or somewhere in that region.
All tracks flown in LNAV however small are G/S not rhumb lines. It would be reasonable to assume that at least for the cruise the aircraft would have flown a constant Mach No. (but not G/S as that is dependent on the upper winds) and changing heading to maintain the G/C track. In which case if you could take the 7th ping arc (use the ATSB yellow arc) and compare the tracks from various waypoints in the north and compare the times to cross the earlier ping arcs. Likewise you should be able to take the last "fix" round about MEKAR and look at the what waypoint(s) tie in with it).
If I was "doing the flight planning" I would have concentrated on the FIR points as turning points as they are handovers between ATC units. Skyvector.com has a good flight planning facility to play around with.