Regarding the Promises, Promises Overture, I believe it's Tunick's work. I've read somewhere that Bachrach was critical of the orchestrations having too much of a Broadway sound, although I think Tunick did an excellent job imitating Bachrach's style. (In the Follies score, there's a tempo marking, I believe for a section of "The Right Girl" that says "a la Bachrach," although that was probably the work of dance arranger John Berkman).
Some composers proposed layouts for their show's Overture, but it's almost always the work of the orchestrator. (I believe though, that the aforementioned Sondheim did actually write his own dance music for "The Cookie Chase" in Anyone Can Whistle, which is somewhat unusual).
Begin at the beginning and go on till you come to the end: then stop.