IT'S a good idea to go to the stage door about 2 hrs before a show, and depending how many people are there some will allow photo's and sign others will not, waiting outside after a matinee is usually a dead loss as if they have an evening show don't usually come out.
I saw Julie Andrews in Victor/Victoria on broadway, there were three people waiting outside she wouldn't sign anything I was told this by shops on broadway, I said good to see you, she snubbed and ignored us, yet she says she
is proud to be british when abroad, Like you I was shocked and disappointed. Did you get a programme if so look to
see who is the manager and I would write enclosing the cost of a programme and SAE and ask if they would sign usually the cast will sign near their name or photo, some signatures are unreadable anyway, for secruity no doubt.
Good Luck