The only copy of the “Big Night” screenplay I can find is in the Volume 2, Number 3 edition of ‘Scenario: The magazine of Screenwriting Art’ which was published in the Fall of 1996. Besides the script, the magazine also provided an “interview” with writers Stanley Tucci and Joseph Tropiano. Interestingly, I can’t find any mention of the final scene in the interview.
I can tell you that the script is radically different from the final scene in the movie. In a conversation I had with Campbell Scott at the Kent Film Festival many years ago, he said the scene as written was too long so they tried a variety of shorter takes. If I remember correctly, I think the final scene was the fifth or sixth take.