There is no need to leave the show early in order to get a good spot. If you really, really book, you can start to edge out as the curtain call is drawing to a close (or even directly after if you can REALLY move!), get to the stagedoor (it's to your left once you exit the theatre), and wiggle your way up to the front of the barricade.
I went on Wednesday; first of all, the show is fantastic--Liev Schreiber, Jessica Hecht, and Michael Cristofer especially doing absolutely brilliant jobs--and Scarlett Johansson is also really very good in her own right. Beautiful set design, too. Anyway, with regards to stagedooring, I left directly after the curtain call and managed to get to the front of the barricade with little trouble... although after I arrived the whole scene got progressively crazier (at one point cars couldn't drive down the street!). Jessica Hecht smiled but didn't sign anything (and, yes, people were audibly asking). Ryan Reynolds came out, by the way, and refused to sign, of course, saying "Not for this--this isn't my thing" (I thought his bothering to say that was very classy and I thought it was sweet to see him there supporting his wife). Liev Schreiber came out next, and he signed for people on both sides of the barricade; he was certainly friendly, and he took his time, so you got to talk to him if there was something you were dying to briefly discuss with him.
Scarlett Johansson came out last; she is unbelievably tiny and very adorable, and she signed for people on both sides of the barricade and took her time and was very sweet--I don't normally bring up outside stuff at stagedoor because it generally feels inappropriate, but I told her that 'Scoop' is my absolute favorite movie of all time and she went "Thank you so much! Really? [laughs] It was really fun to make."
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