My English teacher said that the language in Shakespeare's plays are over the top and exaggerated, and not how people actually spoke at the time.
It's accepted that the stereotypical thespian performances most people associate with Shakespeare are nothing like the contemporary performances.
The British Library has actually done a lot of work with Tudor and Shakespeare historians and produced [this CD](http://shop.bl.uk/mall/productpage.cfm/BritishLibrary/_ISBN_9780712351195%20/353759/Shakespeare's-Original-Pronunciation-(audio-CD) which is pretty much exactly what you're looking for. You can hear snippets of it in this news article
It appears now that an accent which is closest to a current west country (Bristol area) would have been heard, with mixes of Irish and other English regions such as Yorkshire. I'm sorry I don't have an academic paper where they lay all of this out, but I' not aware that there is one, particularly not related to the British Library CD which is the best source of authentic Shakespearean performances.