Are the two Harwood lines related? Or, does another ancestor connect them to explain our matches?

The title of this post poses two questions. The answer to the first one will come with Y-DNA data. Two descendants of the  Concord Harwood line have Y-DNA results in the FTDNA Harwood Project database. A Y-DNA test of the brother of our GC Chr#14 match (alleged to be of the Concord line) does not match those results (John, merchant of London via son Nathaniel); this means that it is likely connected to the Andrew Harwood line instead. As a follow-up, we have identified an Andrew Harwood descendant who has consented to a Y-DNA test; if it matches GC's brother, this will have been proven and we will know that the two lines are not connected. These results should be available by the end of February.

The Andrew Harwood lines we know of that carry the Chr#14 segment, DC2 and MB, converge on a son of James, Jr. and Lydia, namely John Harwood, who married Abigail Hastings; so the source of the Chr#14 segment is to be found in one of their trees.  Abigail Hastings' tree is fairly well understood, however John Harwood's has a major blind spot - we don't know the maiden name of his mother Lydia. Our own paper-trail research of the GC line shows it going back to a Warren Harwood, b.1803, son of Joseph and Elizabeth (unknown surname) Harwood living in Bennington, Vt.  We believe that Joseph (son of John Harwood), who Watson Harwood said moved to Bennington, Vt, is likely GC's connection to the Andrew Harwood line. The 1810 census shows two Joseph Harwood's in Bennington, Vt, one (born between 1766 and 1784) who appears to be Joseph Harwood, b.1781,of the Concord line (whose wife was Vesta Blackmer and was father of Joseph Blackmer Harwood, b. 1809), with five in the household, and the other, who seems too old to be from the Concord line, born before 1766 and having ten in the household.  The older Joseph had three male children under 10, three female children under 10 and one female ten through fifteen; there was also a younger adult, with his presumed wife, in the household in the 26 thru 44 age group (b. 1766-1784); Warren Harwood could be one of the 3 males < 10 years old.  I am assuming that the listed head of household (Joseph) was the eldest male, though it could have been the presumed child of that elder Harwood. The Concord Harwood genealogies show no Joseph in the Bennington Vermont Harwoods until Joseph Harwood, b. 1781, son of Zachariah Harwood.

If our theory regarding GC's line is correct, all three of the Harwoods carrying the Chr#14 segment came down through John Harwood, son of James, Jr. Unless we find another with the Chr#14 segment who was descended from a different child of James, Jr., we have to consider that the segment came down through Abigail Hastings' pedigree. If we do find a Chr#14 segment in another line, the pedigree of the wife of James, Jr., whose maiden name we do not know, is also a possible source of the segment. 

Just recently it was found that some researchers have claimed that Lydia Coolidge, b. 1700 in Watertown, MA, is the wife of James Harwood, Jr; the problem is that we've found no source proving that claim. However, researching the tree of Lydia Coolidge, we can look for a common ancestor who is also in Josiah Proctor's tree. We did this and we found that Lydia Coolidge is a descendant of Ellis Barron, Sr. of Watertown, MA, as is Josiah Proctor. This is not conclusive proof that Ellis Barron, Sr. (or his wife) carried the Chr#14 segment and that Lydia Coolidge was John Harwood's mother, but it certainly makes it a possible explanation.