Ok, now I feel stupid. My new pal Keri Cahill tells me in the comments that I might be interested in her group Rebel Shakespeare, which performs "Shakespeare by kids, for kids". It's a series of summer programs for children as young as 5 years old to learn about Shakespeare, including performances of plays such as Henry V, As You Like It, and Romeo and Juliet.
The thing is she's based in Salem, Massachusetts. I live down the street from Salem, and have spent plenty of summers there. How did I not know about this?!
They appear to be doing As You Like It opposite Commonwealth Shakespeare down on Boston Common. I wonder if that is by design? I have to admit, if I've got to pick a show I'm going to go watch the professionals. At least until my kids are in one of the productions :).