In the more than half-century since “Rocket Man” first shot its way to the top of the charts, it would be safe to assume that Elton John has performed the song hundreds — if not thousands — of times.

Elton John’s 1972 hit “Rocket Man” might seem adequately melancholy on its own, but the short story that inspired it is even more devastating. As has always been the case with John, he wrote the lead ...