Okay, the confusion with the bad merge was caused by the fact that Elizabeth Martin's first cousin husband had the same name as her father.
https://www.geni.com/merge/view?revision_id=68772669260
Looking at the merge, one is almost in line with her father, while the other one is almost in line with her husband. Oddly, the one on the left which looks most like her husband -- had been marked "female" for gender.
The pedigree chart provided by the Museum in NY that is associated with her father's house, is very helpful in sorting them out. As first cousins, her father was the brother of his father, both with the same name "Josiah Martin". So the Geni profile for her father should be this one:
Josiah Martin
According to her father's family pedigree chart:
Maj. Samuel Martin m. Lydia Thomas. He died in 1701 and in 1703 she remarried, to Edward Byam. With her first husband, she had:
Samuel Martin (Josiah Martin's father, 1694-1777)
Josiah Martin (Elizabeth Martin's father, 1699-1778)
William (d. 1735)
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Elizabeth Martin's husband's father Samuel Martin had Josiah Martin plus Samuel Martin MP and Henry Martin MP
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Elizabeth Martin's father Josiah Martin (linked above in this post) married first Elizabeth Chester and with her had three daughters (Lydia, Polly, Mary);
secondly he married in 1735 Mary Yeamans (d.1805) and with her he had 9 children of which Elizabeth (1736-1778) was the eldest of all.
Elizabeth Martin married her first cousin, "Josiah Martin" and they had 8 children of which 4 are named on her family's pedigree chart. It is reported in various sources that some of their children died young and that none of them married (so no legitimate grandchildren for Governor Martin). The children named on the pedigree chart for Elizabeth Martin and her first cousin, Josiah Martin are:
Mary Elizabeth (1762-1820) died unmarried
Alice (b.1768) died unmarried
Samuel (b. 1771) died in NC, unmarried
Augusta (b. 1775) died unmarried
https://www.friendsofrockhall.org/family-trees
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Suzan Martin the document you provided is very helpful. It starts at the top with the man who was the grandfather of both Elizabeth Martin and her first cousin, Josiah Martin. It shows her as being the daughter of "Josiah Martin" and also the wife of "her kinsman, Josiah Martin".
The only problems I see with it are that it doesn't make the connection between her uncle Samuel and her cousin/husband, Governor Josiah Martin. And it doesn't list the children of this couple, who are under discussion here.