An out of town gig would've tightened and polished the text, but wouldn't have addressed the central issue, which is at the conceptual level: the meeting of the three isn't inherently high stakes, and the shared revelations aren't fresh. (Lots of posts above go into this, mine twice). The show had at least two high profile workshops, one with Ebersole one with Mazie, Boyd Gaines attached back then as Huxley. And many readings. So it's not as if Lapine and company didn't open up the process for feedback. But the fixes needed should've been made early: the score, lovely as it is, doesn't always know what should be sung. Certainly the Claire Luce act 2 material, among the most redundant, should've been fixed quite early. (Why doesn't she interact with the two attractive guys? Her husband is emotionally unavailable; instead, she revisits the mother/daughter deaths with the guys off stage; huge focus mistake.) These are substantive content issues to be questioned and corrected in the preliminary writing phase.
It's unlikely that a brand new section would've been written for the second act as late as an out of town gig. The show didn't need "Comedy Tonight" or "Before the Parade Passes by" added; it needed to dramatize shared trips with powerful shared participation among the three disparate players. That was foundational, baked into the DNA of the piece.
"I'm a comedian, but in my spare time, things bother me." Garry Shandling