So as homage to the Master, and explanation to others, I’m repeating here my understanding of the Jedi’s technique.
To lift up, one must push down.
Twist corkscrew in, but stop about a ¼″ before it is fully inserted.

Next, using as much body weight as is necessary (fret not, I have enough), push. The cork is pushed in by that ¼″, which loosens the cork. It de-sticks it from the side of the glass.

Now twist out in the customary manner. Breaks not. Crumbles not. Shatters not, the cork. Drinking, we can start.