Rationalising global location data across several hundred years based on extracting real-world references from complex and metaphor-laden text.
Every single part of that should trigger a 'definitely complicated' warning bell.
No. It is amazing how small his world was. He was born and grew to adulthood, in the world where Spanish dominance kept England from attempting to explore the world. While Jamestown was settled before he died, he never wrote about it.
I've updated my understanding of how (un)aware people were in this era of the larger world. I have no idea why I would have ever expected otherwise.
He may not have written about the British colonies but the New World was clearly at least somewhat present in his mind and his audience's minds.