Gysbreght, any azimuth solution very close to due south will be numerically unstable where very small speed changes cause relatively large azimuth changes. Azimuth solutions are essentially symmetric about north/south, with a small latitude-dependent phase shift that depends also on the flight path angle in non-level flight. A prime example of this instability can be seen in the 1827z BFO cluster.
Solutions in general are not due south. For example at 1941z the choices are about 30 degrees either side of south at normal cruising speeds.
See
http://www.aqqa.org/MH370/models/aqq...muth_v3-5.xlsx for an analytic azimuth model.