It must be like watching the original, unadulterated, completely undigital versions of Star Wars!
In ten days, students at Kansas University will be performing the first original pronunciation performance of Shakespeare to take place in the United States: A Midsummer Night's Dream. I encourage you to watch their video on YouTube, where you can watch them in rehearsal and hear the original rhymes preserved. Click here for a detailed article on the production.
But it's quite a question, does OP make the production more authentic? I think perhaps it does to a certain extent, at least historically speaking. In calling us back to our language's past (as Paul Meier points out in the video, this is the accent the first Americans would have had), there seems to be a sense of the authentic. We tend to value our roots, our origins. This, however, is not the sense of authenticity I am seeking this semester. Not quite. As I mentioned above, if the actors do not present a compelling story, I don't care what sort of English is coming out of their mouths. So it appears I have one small requirement to add to this definition... for something to be authentic, it must be compelling. Well, it's a beginning.