From what I take it the show was very much in flux its entire run, so getting a definite list is likley impossible. Lists from day to day are probably very different, if people who saw the show even remember the songs from only one listen.
It's not because of the changes made during previews. The reason their isn't a song list in the playbill is because they don't want to give any of the suprises away. A lot of people asked Anthony rapp about it during stage dooring and he said it's just like next to normal, some of the song titles can give away some of the suprises so they don't include one
"A Chorus Line" famously used to list the song as "Tits and Ass", and the reaction wasn't as big a deal as they thought it would be. But once they changed it to "Dance: Ten, Looks: Three" and the audience was surprised by the T&A element, the reaction changed dramatically.
"If" - Elizabeth and Company "It's a Sign" – Kate and Company "Make a Map of New York" – Stephen and Company "You Never Know" – Josh "Ain't No Man Manhattan" – Lucas and Company "What the F*CK" – Elizabeth and Company "Here I Go" – Elizabeth and Josh "You Don't Need to Love Me" – Lucas "The Story of Jane" – Kate and Company "If (Reprise)" – Elizabeth "Surprise" – Elizabeth, Josh, Lucas, and Company
Act II
"Walking by a Wedding" – Elizabeth and Company "A Moment Explodes" – Elizabeth and Company "Hey Kid" – Josh "Some Other Me" – Elizabeth and Lucas "Best Worst Mistake" - Lucas and David "I Hate You, I Love You" – Elizabeth and Josh "It's Me and You" – Elizabeth "Just Me and You" – Elizabeth and Stephen "Learn to Live Without" – Elizabeth "No More Wasted Time" – Kate and Anne "What Would You Do?" – David "(Always) Starting Over" – Elizabeth "If (Reprise)" – Elizabeth and Company
She definitely does (she IS the main character) but it never feels like she is. In fact, a lot of the times it felt like she wasn't in that much of a scene!