If my reading of the graphs is correct they are above Vmo for most of the episode. I'm surprised the flight surfaces weren't torn from their hinges.

Vmo incorporates a factor of safety in its specification, so exceeding it is not a "parts fall off the aircraft" event.

Vne is where things start to get scary because it's usually based on flutter, which can catastrophically damage/destroy the aircraft in very short order.

Yes. But it doesn't include full control deflections and certainly not control deflections in opposition to one another. Even at Va rapid control movements and control movements in multiple axes can permently damage the aircraft.

Correct