Roundabout, under Haimes' leadership, was noted both for new works and for revivals of older shows with strikingly new elements (like this season's gender-bending revival of "1776.") He was the first producer to try livestreaming a Broadway show ("She Loves Me" in 2016). And somehow, besides producing lots of shows (and 11 Tony Awards), Haimes also found time to teach at Yale University and Brooklyn College…