“Sweet Caroline” lands right before intermission, and the whole scene is so good (So good! So good! So good!) that this New Yorker almost forgot the song is the anthem for the Boston Red Sox. Book writer and biopic veteran Anthony McCarten (The Theory of Everything, Darkest Hour, Bohemian Rhapsody), also represented on Broadway this season by the Warhol-Basquiat play The Collaboration, places the songs thoughtfully, and for maximum emotional effect: Diamond’s first live performance is acoustic, the melancholy slow burn “Solitary Man.” As his confidence grows onstage, his numbers get bigger and glitzier. Act 2 opens with the wild, soulful “Brother Love’s Traveling Salvation Show,” featuring the singer in full razzle-dazzle, sequin-and-tassel mode and the chorus shimmying for dear life. Combining “Brooklyn Roads” with “America” is a stroke of genius (though bringing in Neil’s bickering parents between verses dampens the mood). And the existential power ballad “I Am…I Said” gets the spot it deserves, as the 11 o’clock number, where it’s sung by Mark Jacoby as present-day Neil, with Swenson joining in at the end.