I have only just found this correspondence, some years after the original postings.I much appreciated your earlier history of the Pole family.I can also confirm your correction regarding Edward the brother of Ann.However, I am sure that he didn't go to America,.He did indeed marry Grace Jones, and all his family were born in England.
His second son John (1705-55) went to America and ended up in Philadelphia (thread about him elsewhere) and the Pole name continued there through him.His youngest son Thomas (who you referred to), left the USA to visit his uncle in England and remained there.After a successful practice in the City of London as a doctor he became better known in Bristol.His only surviving male line also went to America and his daughters of course changed their names through marriage, so the Pole name through this family is only found in America.
I descend from one of Thomas's daughters through ET Wedmore (who you mentioned) - he was my Great grandfather.
Thomas Pole wrote (in a book in my possession) that the Pole family came from Wales.This fits with your comments.You say "Ann Pole and her brother, [Edward], who also came to America, were almost certainly direct descendants of Sir Richard Pole and his wife, ..." apart from family tradition, what evidence have you found linking this family before Edward, the father of Ann and Edward, back to the welsh family.I cannot find where the elder Edward was born.
For more details please see the Wedmore/Pole websitewww.wedmore.org.uk/pole/(which needs an update!)