I've heard two reasons for the half filled boats. One was that most of the passengers gathered on one side of the ship. The other side was almost empty and they had trouble finding people to put in the boats. Instead of trying to find more they just launched the boats as is. The other reason was some of the officers were afraid to load the boats to capacity fearing that they would overload them. I've never heard the boat drill theory before, it seems a little suspect to me since the collision occured late in the voyage.