Ok so you do not have to do anything to have LEAP track hands from any direction.
Reverse orientation is used to change the settings from desk upward point of view to visor downward point of view.
The visor view takes into consideration the movement of the camera with the head and that the back of the hands orientation should be considered before the palm sides to identify left and right hands.
The desk-up view presumes a fixed position camera and the palm sides are expected.
This is for processing efficiency. If your hands are not as expected it will adjust to them.
Regarding the design of your system, the virtual button is actually switching from Player 1 is active to Player 2 is active and you should simply program accordingly.
You could experiment with the axis orientations for Player 1 and Player 2 if there are still issues.
You could try starting the game with all 4 hands in camera range and only allowing one player to act at a time. No button would be required
If you can't get interaction engine to handle multiplayer well, then I would suggest multi-camera solutions.
To increase efficiency, you might try to use the camera from the desk side.