Shlomo Carlebach might not be a household name (at least not in non-Orthodox Jewish households, or in households that are even a few miles from the Carlebach Shul on West 79th Street), but his approach to synagogue worship was both revolutionary and enormously influential. An early Schneerson follower, he was prominent in the baal teshuvah movement (in which a comparatively secular Jew "turns" toward Orthodoxy), and instrumental (pun intended) in infusing the contemporary worship service with music. If you've ever been to a synagogue service--whether Orthodox, Conservative, Reconstructionist, or Reform--in which congregants sing ecstatically, dance in the aisles, and intone extensive niggunim (Hasidic chants), you've likely witnessed Carlebach's influence whether you knew it or not. A devout Jew who devoted his life to outreach through music, Carlebach would seem to serve naturally as a central character in a musical.
