But working with the director-choreographer Casey Nicholaw, who staged 'Chaperone' as well as the current 'Aladdin' and 'Mean Girls,' the team behind 'The Prom' has attempted a more difficult gymnastic maneuver. As in many of the greatest Golden Age musicals, they latch onto a subject of topical importance, using its gravity to anchor their satire and their satire to leaven its earnestness. In full 'Hairspray' mode, they mostly succeed.