That's very interesting indeed. I think I heard that today's Virginia accent is most faithful to the original.
The stereotypical English Accent (clipped, haughty, veddy veddy proper) is a very recent construct (not much more than 100 years). It's called Received Pronouncuation (or BBC English) and it was created for reasons of class. It was (still is) something that has to be learned and acquired. Americans think it is the natural way the British speak, but it's something they have chosen -- lower classes in England are easy to spot because they don't talk in RP. This allows the "best people" to easily recognize each other.
British language changed and affectations abounded after the 15th century. For example, Americans use the hard r, as the Elizabethans did; today, it has practically disappeared among upper class Brits. Thus you have mothah for mother, fathah for father, rathah for rather, Chahles for Charles, chuch for church, etc. Also the a as in our cat, has been softened.
I can't name or specifically locate them, but there are several places on the left coast where the dialect is very close to what came over from England;
and very unlike today's UK.
On a related note, having finally visited the UK, there is as much or more regional dialect variation on that one island as there is in the entire USA.
Today I'm afraid Shakespeare would have had to draw pictures.
An interested notion, although as not a native English speaker, I have trouble analysing different dialects, except those that have the most differences. I can different through a few broad though, like a vague English one, a vague celtic (Irish and scottish) one, a general American one, and a southern/Astralian one, and of course the Indian/Pakistani.
Here in Iceland we don´t have any dialects, due to the smallness of the nation, the long time rule that you could not marry anyone more related to you than in the sixth generation, resulting in people having to go far to find a suitable mate (and maybe resulting in our girls beeing viewed as extremely beutiful, yeat another time Miss World is ours) and specially the long litterary tradition here dating from the 12. century.
There was a small variation in different parts of the nation, but those disapeared into a certein neutral speak where the certein variations all but disapeared, because the people in all the other parts of the country spoke the same in these wovels and such.
Actually there was a certein local dialect much frowned upon in the east and it was conciously eradicated, by the government (schools and radio) as it also made it more difficult for those speakers to write proper Icelandic, as they had trouble differenting between e and i. Weather it was a good thing or bad I am not sure, but it at least helped to ensure a national unity when it comes to the language.
And as a side note, Icelanders view their language as the same (or nearly so) as the Vikings spoke and we see all the other nordic languages (even German in some sense) as a corrupted by external influences that we could preserve Icelandic from over the ages. So we see all the nordic languages as a dialect from Icelandic, at least jokingly.
But a language can be an indicator of the history of people´s and places, so it is interesting to note that the US has preserved many thing lost to Europe. Come to think of it, the people that still speak Icelandic in New Iceland (or Gimli) up in Canada (settled by Icelanders in the 19. century) have this very beutiful language, maybe not dialicticly, but the old words and good old ways of how they put together sentences.
And I beliewe the Icelanders there are more rooted in the old Icelandic christian values, free-loving nature of our Originals and even national pride.