Pronunciation definitely was different in C16/C17 from what it is now - on the radio today, I heard a reconstruction of part of Romeo and Juliet as they believe it was spoken in Shakespeare's day, and it sounded like a West-country accent!

However, a lot might depend from whereabouts in England the writer (or his parents) had emigrated. If they had come from the northern or north Midland counties of England, then "up" would almost certainly have been pronounced "oop" - as it still is today in those parts.