Now you can see the actual "hit" of the shot. It has been saved up to this point. Now the true hit is actually a turning or twisting of the hand that twists the hand and forearm and torques the racket through the ball. Rather than brush over the ball, you are grabbing the ball with your strings and twisting it off to the side.

Watch Heuberger's hand. His hand is driving this motion. He is turning the racket up to the ball with his hand which causes the hand and forearm to prontate and turn over.

In the bottom image, look at the two side by side pictures. In the picture on the left, we can see Heuberger's knucles and the top of his forearm. In the second picture on the right, both his hand and forearm have twisted to the opposite side. Now we see the back of his hand and the underside of his forearm.

UPDATE:

I am a huge fan of Dave Smith's work. His philosophy mirrors mine very closely (we both believe that change in technique is the very achievable secret to rapid improvement) and I think he is one of the great "teachers" of the game. He writes for TennisOne and has a superb book called Tennis Mastery.

Dave pointed out to me that a big problem people have with the kick serve is that they rotate their shoulders through the shot. Let me quote Dave here:

"If the body rotates open too early, the player can't pronate and hit up and to the right. (Nearly impossible, anyway!) On the ad court, this results in the player having to hit only a flat serve (the only way they will be able to direct the serve into the court.)

You might want to point out the significant aspect of the kick serve and in your video clip, that Hueberger's upper body stays very sideways with the hitting elbow well back (relative to the center line of his body or his head for easier reference), and the significant 'pulling' action of the toss arm around the front of his body, pulling in to hold the upper body sideways and to prevent the toss shoulder from opening up.

Until players recognize this body position which allows the racquet to do all the things you covered in the tip, (namely hit up and out, up the inside of the ball or, as you said it in the tip, 'grabbing the ball and twisting it off to the side), they won't see the results that they are seeking."

Dave Smith, Senior Editor TennisOne
Author, TENNIS MASTERY
Wilson Premier Advisory Staff
Owner, St. George Tennis Academy