As I was reading this thread, I thought of my high school doing a production of Dirty Rotten Scoundrels. I nearly peed my pants. Ruprecht...
I'm not seeing a lot of shows running currently on Broadway that would be able to fit the "high school" stage. For example, every musical you've stated including Rent, Producers and Avenue Q- even Wicked- probably won't go well with schools. I haven't heard any school, as far as I know, doing Mamma Mia! Is that released yet? I really wouldn't know, but I could imagine that to be one of the few that could be seen done by students.
I think the best high school musical (well best musical that could be done run by students) is Once Upon a Mattress. My school did that a year ago and a regional theatre is doing it this coming up April.
"I haven't got a pail."
"Find your grail, your GRAIL!"
"But it's not missing. It's right on the counter where it's supposed to- defying gravity, my giant cup's gone!"
"Five hundred, twenty-five thousand, six hundred minutes. How do you measure... measure a year?"
"How many times do I have to tell you, it's five hundred twenty-five thousand, five hundred and eighty-five point thirty-two minutes. You will never graduate if you keep basing your math on showtunes."
"You ruin Broadway for me."
"As well I should."