I found this article that poses the time travel question amusing not because Gina Accorsi says “probably towards the time Shakespeare lived,” but because of her rationale: “There seems to have been less conflict back then.”
Methinks she doth assume too much. From what I understand it was quite the battleground at the time between the Catholics and the Protestants, and more than one biographer has tried to make the case that one reason we know so little about Shakespeare is that he deliberately kept a low profile for fear of being branded a traitor and meeting quite a nasty fate.