>Global, I wouldn't ask them to sign a poster/photo from the movies they were in. Playbill or windcard would be okay.
What I often do is to ask a performer to autograph on my ticket. I just went through those old tickets and found the symphony tix autographed by Stokes (it was a concert) in 1998.
I don't usually do stagedoor anymore unless someone I know is in the show. But when POTO was in SF, I got to know one of the ensemble members so I went to the stagedoor and got autographs from the cast. One time I was asked if I'd like to see the backstage. Would I like?!! We went on the stage, peeked at the Phantom chair (we couldn't touch anything), went under the stage and saw all the costume etc. It was FUN!
Re: Patti taking nap between matinee and evening shows, I totally believe it and she should do that. When my friend was in a show, in which he was on the stage all the time (literary 100% of the time) singing and talking while he was on the stage, he took a nap between the shows. And he didn't even talk during this time either to save his voice. We communicated by signing and writing, boy that was fun
I never had a bad experience at stagedoor except once or twice I couldn't catch the performer (already left the theatre).