That's a good point about the "Babylon has fallen" message. They should really be ramping up that message if they believe it the precursor, the thing that lets everyone know that the JWs were right, so that they know who to go to for the last minute repentance. It's great how you've connected the dots. I wonder how many JWs will do the same, saying, "If that's the case, shouldn't we be pressing home the XYZ message?" Do you foresee any such message becoming the new focus, or has the GB simply failed to realise the implications of their own doctrinal change?
In mainstream Christianity, last minute repentance is generally referred to as a "deathbed confession". A person goes through life "sinning" and then "give their life to Christ" when they know it's all ending. The episode of Blackadder where he is the archbishop of Canterbury gives an example of how it worked in those days.