I think part of your complaint with the terms arises from your apparent view that the Singularity event will be slow enough (relatively) that people will be able to keep up with it as it occurs.

This isn't necessarily going to be the case, particularly if the Singularity ends up being driven by some form of rapidly self-improving process. In such a "hard takeoff" scenario the term Singularity comes very close to matching its mathematical roots, and indeed in such a case you will be able to look back from the future and say "yep, there was the period of 75.8 hours in 2018 when things changed".

I think also that Vinge was speaking of a specific event when he coined the term. He was speaking of the moment when a greater-than-human intelligence is created one way or another. So again we are speaking of an actual specific moment in history after which things are irrevocably different.

So in my opinion you may be grasping here for a new term that will not actually apply to what could end up occuring in the future. You're looking for a term to represent some sort of "slow Singularity" which may or may not occur, but which I think is something different than what Vinge and others may be imagining when they use the term Singularity.