I've discovered a solution to make this easier. Go to options on the pause menu and change the controller settings:
- camera sensitivity: set it to 1 (default is 10)
- grip mode: set it to toggle
With these settings it was a lot easier as it was harder to mess up with the right stick and I did not have to hold the right trigger to control the ball.
Additionally, I have also added at the end of this solution a link to a video from achievement hunter that should help as well. Just remember that, for the third puzzle, you do not need to rush at the disappearing section as he did in the video. If the ball is in the middle while you are moving it, you can just wait until the line reappears, and the ball will not fall.
(note on 03/28/2020: I've udated the link as the old one was no longer pointing to the video)