"I still don't understand all the palaver and releasing that northern arc if they had strong indications that the plane went south though. The whole investigation seems to have been a shambles so far"
But the arcs were in relation to that piece of evidence collated with the flying time of the plane. Those two matters were "hard" evidence (assuming no tankering extending the flight distance circle).
In terms of likelihood, depending what info they had from land based radar (which if some was given was probably in strict secrecy) they could probably reach the conclusion it was possible but unlikely that the plane had avoided radar detection - meaning the simplest explanation is that it wasn't there ie that it was over the sea.
. I am sure the Chinese wouldn't have searched a land corridor if they knew definitively the plane wasn't there (of course, they may have announced a search and not done it if they did know that)
However this turns out, surely running searches in parallel was better than exploring one possibility then another sequentially.