When I became interested in Moore genealogy back in 1976, I began looking to Stephen's ancestors, and in particular his father, Col. John Moore of New York City. Thus, I wrote to Trinity Church for information in 1977 and this was the reply:
John Moore, Esq. (1745-1828), the grandson of Col. John Moore of New York City, wrote on 29th April 1821:
The John Moore vault is in the Sec. S.3.
1) John Moore, Esq. died 29 Oct 1749...was the first corpse interred in family vault South side of Trinity Church.
2) His wife Frances Lambert died 1782 March
3) Rebecca Moore [daughter of John & Frances]
4) Susannah (Moore) wife of John Smyth of NY
5) Lambert Moore
6) Thomas Moore 1784
7) Elizabeth (Channing) Moore 1805
8) Daniel Moore, Capt of British man of war, killed at sea 1777
9) Judith (Livingston) Moore, daughter of James Livingston, Esq. of Poughkeepsie, 1813
10) John Moore died 1828
11) Magdalen M. Onderdonk, died Oct 1836. Moved from St. Ann's Ground, Brooklyn, 3/16/1860. [She was a daughter of Lambert Moore.]
12) Jane (Holland) Moore died 14 June 1767. [First wife of Lambert Moore]