Thanks for these links, very interesting. It seems that the key to the analysis is that the satellite itself wanders in a figure of eight motion so its relative motion to the plane and the corresponding Doppler shifts help to eliminate the northern route alternative. The four week duration for the black box signal must surely be a minimum specification so you would normally expect a couple of weeks longer but even so the range is limited and in deep water you'd have to be right on top of it to locate it. The link below states that if the plane had been doing 310 knots at 12,000 ft then the crash site would be in a completely different location.
http://www.slate.com/articles/technology/future_tense/2014/03/evidence_that_flight_mh370_crashed_in_the_southern_ocean_doppler_effect.2.html