Yes, we seem to be talking about the same John Heaney. Late last night I came across an online tree that had Thomas & Ann Heaney buried somewhere in Galway which is totally incorrect- they are buried in Aghadowey.
The Heaneys were from Cullycapple townland in Aghadowey Parish- you'll see that it marches Mullaghinch townland:
https://www.townlands.ie/derry/cullycapple/There were also Heneys (no a) in Cullycapple who are
NOT related but due to spelling variations the 2 families can get confused. Also, I've see some bad transcriptions which give the surname as Henry which is incorrect.
Starting with John's obituary in the Coleraine Chronicle (28 Feb.1863): At his residence, West 37th Street, near 10th Avenue, New York, on the 10th inst., John, eldest son of Mr. Thomas Heaney, Cullycapple, Aghadowey, aged 35 years.
Outline family tree (your details which I didn't have previously in
red)
___ Heaney (d.before 1833), Cullycapple
1. William Heaney (c1803-1868), teacher, m. Sarah (c1799-1893). Children- Nancy (c1831-1911), Mary Ann (c1836-1925), child, William (c1842-1920), Thomas (c1843-1923), Hannah (c1848-
1928). Only William & Hannah married and the only (two) surviving descendants are elderly & childless.
2. Ann Heaney (c1815-1902), unmarried.
3. Thomas Heaney (c1801-1874), farmer, m.Annie/
Ann Thomson (c1805-1896). There were Thomsons in Cullycapple but she is much more likely to have been one of the Glasgort family
1. John Heaney (1827-1863 N.Y.), eldest son
2. William
? Heaney
3. Thomas Heaney (c1837-1919), 3rd son, m.(1879) Catherine McQuigg. Children- Anna Bella (1880-1905), Thomas James (1882-1949).
Neither child had family so this line has died out. 4. daughter ?
Ann Heaney m. John Hogg 5.
Daniel Thomson Heaney (1842), N.Y. 6. Robert Alexander Heaney (1845-1856), youngest son
7. Jane Heaney (d.7 Jan.1871 Cullycapple) m. James Aughey- child: James.
Robert Heaney (c1785-1871), farmer, Cullycapple,
m. Jane Wallace (c1788-5 Feb.1867 Cullycapple). There were Wallaces in
Cullycapple & in Mullahinch
1. Daniel Heaney, farmer, m.(1846) Nancy Hull
2. Isabella Heaney (c1823-1900) m.(1866) Joseph Hunter- no family
3. Ann Heaney m. ___
4. Peggy Heaney, youngest daughter, m.(1852) Thomas Boyd- family
Also in Cullycapple-
Daniel Heaney, farmer, m. Mary (c1796-1862)
1. Mary Jane Heaney m.(1848) John Moon
2. Margaret Heaney m.(1855) John Doherty
3. Sarah Anne Heaney, youngest daughter, m.(1863) Robert Mayben
I lived in Cullycapple before I married and can expand more on all of the above if you wish. I'll also go see Hannah Heaney's grandson to see if he can add to my own notes.