If you're really patient you could just buy a Rent poster and get it signed by the original cast when they are in a show. They're all going to be doing something in the city again sometime. People buy autographed posters all the time- for a lot more than you're suggesting- specifically because they know how much effort it would take to hunt down every performer in a show, and it is worth the cost to have someone else do the work for them.
And if you think it's that easy to find Byron Utley and Aiko Nakasone, I'll pay you less than $200 for that OBC signed poster myself.
Like a firework unexploded
Wanting life but never
knowing how