Just had a quick look at this and it seems as though it would be fairly easy to reverse the original top card in the centre of the deck therefore giving the cut some purpose.
You would have to tip the hands slightly so that the front edges don't flash. Begin the cut as you did with the first two packets and as you rotate the third one round and it is parallel with the first two, the fingers of the left hand can reach across and pull the original top card flush with the bottom of the left hand packet as the right completes the rotation.
You should now have one card reversed in the centre of the deck.
Hope I have explained this well enough for you to understand. Try it with a deck and I am sure you will see what I mean.