First of all, I second Rico, Head Games will definitely help. I'll also agree with what others have said about practice. Confidence is born out of success, and success is gained after a lot of practice. Confidence is hard to fake when you're in an unfamiliar situation, however some people do have the balls to make an educated guess and totally commit to it. Now at the same time, educated guesses are built a lot off of previous experiences, the more experience you have, the more confident you are in moving into unfamiliar territory.
However, making a mental move is different from trying to do something unfamiliar physically. But like Rico says, there shouldn't be any reason to move that much during a 3 game league set. That tells me they have bigger problems than not being able to adjust. If they start out league with a 2000 grit Hyper Cell, I don't feel sorry for them. I rarely move more than 2 or 3 boards a night, but I manage transition the best I can and stay away from people that are throwing chalk monsters.
People will always feel more comfortable doing what they know, but if they're moving left because their ball is hooking, if they move into the right area they really shouldn't have to change much about how they're throwing the ball because they still have all that friction they created to bump. I was teaching my wife how to manage and use her own transition to her benefit, and throughout the games she bowled, she never had to change a thing about the way she was throwing the ball because I was showing her how to use angles and her created friction to her advantage. Also, you don't always have to bump your friction, you can move EVERYTHING left and use your previous track as a safety net. Sometimes perception ISN'T reality. If someone has to move because the friction has moved, that changes certain definitions. Just because you're moving deeper doesn't really mean you're hooking any more of the lane . . your ball may be covering more boards, but that doesn't mean you should have to change your game significantly, especially just to get through a 3 game league set.