The biggest problem with Broadway proshots is that most productions generally have niche fandoms, especially compared to pop stars like Swift or Beyonce. And the ones that have broken out with the GA already have successful film adaptations (Chicago, Les Miserables, West Side Story) or already have proshots available on DVD (Phantom of the Opera).
So apart from Hamilton, there's not much you can really capitalize on. At least if you want something more than a Fathom Event showing. Maybe Lion King, because it's so different from the animated movies? But that's all I can really think of.