I have no hesitation to sit 4th liners after a good game. 10 minutes of honest hard work should be an assumed performance. Sitting a guy like Beagle should make him hungry when he gets back, he wont be going through the I have a job motions. There are no ego's to shatter on 4.
Backstrom got demoted (alleged inadvertantly even though he was scoreless IIRC) to the 4th line for a game and it was a spring board for his career. One can hope doing so with MJ will spark him, get him in a place with no pressure to score.