SNGF: My Father's Mother's Paternal Line

It's Saturday Night Genealogy Fun (SNGF) night again. Randy Seaver's challenge for tonight is to answer the following questions:

1)What was your father's mother's name?
2) What is your father's mother's patrilineal line? That is, her father's father's father's ... back to the most distant male ancestor in that line?
3) Can you identify male sibling(s) of your father's mother, and any living male descendants from those male sibling(s)? If so, you have a candidate to do a Y-DNA test on that patrilineal line. If not, you may have to find male siblings, and their descendants, of  the next generation back, or even further.
4)  Tell us about it in your own blog post, or in a comment on this post, or in a Facebook or Google Plus post.

1) My father, Alva Curtis SHARP (1917-1978), was the second son of Harold Herbert SHARP (1893-1934) and Virginia Corine MELDRUM (1896-1980).

2) Virginia MELDRUM's paternal line is as follows:
     -father = David James MELDRUM, Jr. (1867-ca.1908)
     -grandfather = James Braithwaite MELDRUM (1840-1876)
     -great-grandfather = David MELDRUM (1819-1901)
     -gggf = Unknown

3a) Virginia MELDRUM had two brothers and one sister:
     -John Harvey Sonnen MELDRUM (1899-1989) married at least twice, but I don't see any sign of children from either marriage in census or other records. The obituary I have for him is minimal, thanks to his being a member of the Neptune Society.
     -Curtis Braithwaite MELDRUM (1904-1975) married Gladys W. WOOLLEY in Harris County, Texas in 1930. They had two daughters. No Y-DNA there.

3b) Stepping back a generation, David James MELDRUM had two brothers and a sister.
     -William L. MELDRUM (1869-?) I lose after the 1900 census, when he's living with his mother, who is now on her third marriage. He is now 30 years old and still single, working as a gardener (following his father's and grandfather's occupation).
     -John H. MELDRUM (1870-1894) died unmarried of tuberculosis.

3c) Stepping back yet another generation, James Braithwaite MELDRUM only had one brother, William MELDRUM, who died just before his first birthday back in Leeds, England, before the family emigrated to the United States.

4) You're reading my blog post, which turns up ZERO candidates for MELDRUM Y-DNA from my father's mother's line. Bummer.