All this time I have been trying to do the trick by pushing down into the pole with my bottom hand. It turns out you have to push away from the pole instead of pushing down. You also have to keep your elbow and fist parallel with the floor. The minute it points down, you lose the grip. And in spite of how it looks in the picture, this trick is much easier when you twist your chest away from the pole rather than facing it.
She also taught me a way to learn the grip for this move from an invert:
All this time I've been trying to learn it from the floor standing up and kicking up into it. It's much easier to invert and twist toward the pole and slowly slide your legs off the pole to your ankles.
Granted I have not mastered either of these tricks yet. But she gave me all the tools I need to practice on my own until I build the strength and courage to do them. I'm so excited!