Any additional information that might have once been on the front of the tomb was gone, leaving me to wonder which Greenleaf (or Greenleafs) were buried there, and who Appleton and Woodward were?
So some time after returning hme, I started looking into this question. Being that this cemetery was in Quincy, my first stop for possible information was NEHGS' American Ancestors site. I found the following information in their database, Cemetery Transcriptions from the NEHGS Manuscript Collections:
- Greenleaf : 436+; Greenleaf (Tomb) Daniel & Thomas (with Dr. E. Woodward & _____ Appleton)
- Appleton : 436; Greenleaf & Dr. E. Woodward (Tomb)
- Woodward : 436; Dr. E. (Tomb) (with Appleton & Greenleaf)
So at this point, I'm still a little vague on Appleton, but I have the names Daniel Greenleaf, Thomas Greenleaf, and Dr. E. Woodward. I actually ended up going back to one of the Greenleaf genealogies, in this case the 1896 edition by James Edward Greenleaf , to see if these names might give me a hint as to the families buried here.
I found the above:
Thomas Greenleaf (1767-1854) whose sister, Elizabeth Greenleaf (1865-1839), married her cousin, Daniel Greenleaf (1762-1853). And Thomas' two daughters, (1) Elizabeth (1794-1854) who married William Greenleaf Appleton, and (2) Mary Ann (b.1796) who married Dr. Ebenezer Woodward.
Heading back to American Ancestors, I located information in their Quincy, MA: Church Records, 1762-1870  database, that confirmed for me:
- Dr. Ebenezer Woodward married Mary Ann Wroe Greenleaf on 13 Nov 1837.
- William G. Appleton married Elizabeth Greenleaf on 19 Feb. 1835.
- Daniel Greenleaf (1762-1853) and wife Elizabeth Greenleaf (1765-1839)
- Thomas Greenleaf (1767-1854) and wife Mary Price (d.1855), and children:
- Ezekiel Price Greenleaf (1790-1886)
- Elizabeth Greenleaf (1794-1885) and husband William Greenleaf Appleton
- Mary Ann Greenleaf (b.1796) and husband Ebenezer Woodward (b.1798)
I am still looking into this, trying to find any additional records for Hancock Cemetery that might confirm my hypothesis.
 Cemetery Transcriptions from the NEHGS Manuscript Collections. (Online database. AmericanAncestors.org, New England Historic Genealogical Society, 2002.)
 Greenleaf, James Edward. Genealogy of the Greenleaf Family. Boston: Frank Wood, Printer, 1896. p. 210. Online. Internet Archive : http://www.archive.org/stream/genealogygreenl00greegoog. Accessed 29 Aug 2011.
 Quincy, MA: Church records, 1762-1870. (Online database: AmericanAncestors.org, New England Historic Genealogical Society, 2005), (Unpublished transcription by Waldo C. Sprague from original records held at the Randolph Town Hall, donated from the estate of Mr. Sprague to NEHGS in 1962)