Didn't Charles Strouse write an unproduced Star Wars musical in the 80s, which was killed by Lucasfilm? I would love to hear more of that score than "Han's Your Man," just for curiosity value.
I think Disney will likely pursue a Star Wars stage show at some point, but I don't know what composer I would put on the project. Star Wars, the original trilogy in particular, is "a story that sings" in an obvious way. The plot is relatively simple and linear, but contains obvious moments of emotional and story highs, the characters are archetypes with some individuating personality, and for being some of the original "big action movies," the big action sequences are primarily only one or two per film, with character melodrama driving the rest of the story.
When you look at it that way, the Star Wars Trilogy feels like Wagnerian opera more than anything else. For a story like that, and a franchise like that, you want a creative team that understands both the mainstream appeal and the grandiose, slightly elevated tone of the material. Perhaps the person for the job would be Disney alum Stephen Schwartz: he's devoted the second half of his career to mixing a big, Wagnerian-operatic sound with more traditional musical theatre.