I have read your posting number 19917.I am the sixth great grandson of Peter Bayes/Bays I, and I am the great grandson of Nancy Carter Bays.
It appears that as far back as 1700 the Bays family and the Carter family knew each other.We know that our Carters descended from Capt. Thomas Carter and Katherine Dale, his wife, that her father, Maj. Edward Dale, was so opposed to the Cromwell government back in England that he came to America as one of the very early English families.
As to Bays, I have no problem with Bays from Peter I on down to my own family, but I am unsure of Peter's parents and his siblings and their spouses.
If you have not already done so, you need to access the "Baze family genea. forum" and postings 469, 484, 494, 505 and 508 by Mark Baze.The two of you need to get together.
If you can furnish data as to Peter's parents, and siblings and their spouses, please advise.