In his frequent visits to Joe’s Pub, writer-composer-performer Ethan Lipton has sometimes shared clever, unassuming musicals that compressed big subjects like space travel and AI into storytelling cabarets. He goes wider in scale—and moves to one of the Public’s larger stages—with this musical adaptation of Thornton Wilder’s rule-shattering, Pulitzer-winning 1942 allegory The Skin of Our Teeth, which takes a New Jersey family from the Ice Age to the end of the world. (Kander and Ebb tried for years to adapt the same play, without much success.) Lipton’s usual director, Leigh Silverman (Suffs), navigates the transhistorical madness with help and ace cast led by Shuler Hensley, Ruthie Ann Miles, Micaela Diamond, Damon Daunno, Amina Faye, Ally Bonino and Andy Grotelueschen.