@rh200,
Could the logs just be time tagged when the ping was recieved.
You are absolutely right. That timing will produce a position line (in this case a curved one) and the originating signal will be somewhere along that line.
IMHO that is the clear reason why the authorities are talking about either to the NW or the SW. If the reason to go SW was a "terminal" one, then a very deep spot in the Indian Ocean would be a likely outcome. The reason to go NW, would probably be politically based. Take your pick.