It's never easy with a big class and the ideas you're using sound good.
I don't think it's a matter of finding activities for the whole class but rather approaching the class in a different manner, using traditional (quiet!) ideas which your boss will approve of but organising them in a manner which keeps the whole class involved:
* speaking quietly when giving instructions so everyone must listen
* mixing groups
* getting groups to do peer marking and so on
Take a look
here where there are a few more strategies which might be useful.