DecemberDolphin said: "Not necessarily heavy on acting, but opportunities in which a guitarist has a role on the stage, ie; School of Rock, Rock of Ages, etc. Not opposed to pit work but enjoy the live on stage performance aspect very much."
It seems like the best thing you can try to do is to try and get into subbing for pits that play live on stage (Jagged Little Pill, Waitress, etc.). You need to get to know Broadway musicians, conductors, and music directors. Join the musicians union, AFM Local 802, and you can get access to these networks. There isn't a formal application process, it's 100% network and getting the right people to know that you're a guitarist that wants to play in pits. Do know that it's a very high caliber job and not something for the casual guitarist, and sight-reading/quick learning skills are essential.