A lot of stage managers I know have worked at Disney, but most of the positions are full time, and there are lot of politics about union, management, versus just employee - I am not sure if it is something you are passionate about - but it can get frustrating at times for certain people . . . other people LOVE their time working at the park.
You should always shadow. South Coast Repertory is a regional theater close, there are lots of road houses in Southern California as well.