Hi there, I came across your post and thought you may want some information I have.I was looking through my paperwork and have a John Stockley in VA, I don't have anything more about Francis but I noticed a difference with his wife Elizabeth's last name. Here is what I have:
"How did this Stokley Family come to America? Most likely, this Stokley line came from Descendants of John Stockley and Elizabeth Woodman.They named one of their sons Woodman Stockley.The same name has been passed down to sons through their many descandants and was also given to our Jacob's son, Woodman, who was born in 1864.The following information was provided by Carol Stoakley from Pennsylvania.It was researched by a Stockley from Tennessee:"
"John Stockley first appeared as an investor in The Virginia Company in 1609.Others of the same name appeared in 1617 and 1620.This John and his brother Francis came to Virginia about 1643 and settled in Northhampton Co VA.He returned to England and brought back 52 settlers on whom he filed as head rights in 1663.He married Elizabeth Woodman in England and they had 11 children named in his will in Accomac Co VA in 1673.John became a man of influence and was elected to Grand Jury and the northern county Vestry before he died.Virkus, in 'Immigrant Ancestors' lists him as born in England C. 1621, a Gentleman.Burgess in Va (probably elected but did not serve because of death the next year.)The birth of John Stockley can be found in Burslem Parish Register, Staffordshire, in 1619, and another of the same name in Lancastershire in 1623, both sons of Richard Stockley.This Genealogy follows to the Stockleys who settled on Corona Landing on the Mississippi River in 1800's and in nearby Memphis, TN. However parts of this family stayed in Va and some probably moved to Delaware. (Henry Walker Stockley po box in Memphis, TN)"
I don't know if this will help you any or even interest you but I relish any tidbit I can get so I thought I would pass it along.Just a little note my gggrandfather was Woodman Stokley.Good luck in your quest!