Switch the transponder on and fly at the cruise attitude.
Even if some warship picks you up, nobody will think to match your transponder code to that of the plane lost on the other side of the world.
I don't agree. Modern radar systems have recorders, and those would certainly have been analyzed.
Again, in the whole middle of the Indian Ocean sits
Diego Garcia, a huge US military naval base notably used for aircraft carriers maintenance. If a place has good long-range military radars, that's this one.
So we can assume the plane didn't flew over there, which reinforces the southern path theory.
Far in the South are the French Southern and Antartic Land. Those islands are small, the climate is cold and windy, and are basically ancient volcanoes getting out of the sea. Not a place to land a jet. Still, there is :
Saint-Paul & New-Amsterdam islands : 2 islands. 66 km². 20 permanent inhabitants. There's not even enough room for a runway strip.
Kerguelen islands : more than 300 "islands". Some barely more than reefs. 7215 km². 45 inhabitants, all located in Port-aux-Français, a logistic, surveillance and scientific outpost. Daunting cracked terrain with fjords everywhere. Mount Ross culminates at 1850 meters over Grande-Terre, the main island. The ideal place if I had to hide a nuclear submarine. But not a plane.
Crozet islands : 5 islands, and some reefs. 352 km². 23 inhabitants. Volcanic terrain again. Average temperature : 5°C. Winds are very often over 100 km/h. Not a suitable place to land a jet.
South of Kerguelen islands, you have the Australian
Heart & McDonald islands. 372 km² of volcanic, icy terrain. No inhabitants.
West of the Crozet islands are the
Prince Edward islands, owned by South Africa. 2 islands, 335 km² of volcanic terrain, only visited by scientific teams from time to time. Again, nothing to do with a jet here.
BTW, southwards lies Antartica. I wonder if you could find a plain of ice long enough to land an airliner. But I don't see the point at all, you can't expect to survive a long time there.
And here's a map of all the 634 runways long enough (5,000 feet) to theorically allow MAF-370 to land, and located in a 2,200 nm radius :