RE: Old Mt.Ida Cemetery Regarding Oakwood, they might have a record with dates for Nathaniel that would clarify which one he is. The FHL reel sounds like it's of the Troy Burial Records; if it said Old Mount Ida, that's somewhat ambiguous. Old Mount Ida was a burying ground at the foot of Cypress St; Mount Ida on Pawling Avenue over time became referred to as Old Mount Ida even though that's not its official name.
John Converse at "Old" Mount Ida on Pawling incidentally would seem to be a reinterment because he died in 1831 and the Pawling Ave cemetery wasn't purchased until January 1832 and wasn't surveyed and apparently not laid out until October 1832.
RE: Old Mt.Ida Cemetery I had not noticed another Converse stone near John Converse's monument. His inscription is so worn, I wouldn't exclude the possibility that one of the seemingly blank sides had an inscription for other family members. There's also a lot of buried headstones in the cemetery.
Are you sure your Nathaniel Converse is buried in Oakwood cemetery? It wasn't established until 1848 so if he's there he'd have to be a reinterment from somewhere else. Are you sure Abigail Lawrence Converse is buried in Old Mt. Ida Cemetery? The DAR in their 1923 survey don't seem to have recorded a stone for her http://www.onentofl.com/tcsnyrenTROYmida3.html
RE: Elizabeth Haynes Lawrence memorial Glad you figured it out. I'm not related although I have Converse ancestors. I just added the gate shot for Wales #1, which goes automatically to all the entries in that cemetery.
Samuel King 1667 - 1713 I was at Old Town Cemetery today, and did not see this grave. A number of the markers have been obscured by weather (or lost). If you can obtain a map or location from the cemetery, I would be happy to go back and photograph whatever is there.