Hi Eleanor, I responded by email, but I'll add a few notes here.
The Rev. Bostwick has a baptism documented as Hermanus Burzee, baptized 05 Apr 1789, Great Barrington, son of John Burzee and 'Mary'. Rev. Bostwick always used the surname spelling 'Burzee' in documenting his baptisms, but was not always known to use the correct or accurate given name for the spouse.
In the book titled 'Register of the General Society of the War of 1812. Washington, D.C.: The Society, 1972, 710 pgs.', the author traces the ancestry of William Edgar Bresee back to his great grandfather, Harmon Bresee, born 21 Dec 1788, who married Polly Post 1813 in Davenport, Delaware, NY.
In my opinion, this clinches the fact that Hermanus Burzee of the baptism record and Harmon Bresee of the 'War of 1812' record are one and the same.
Now, a bit on Harmon's ancestry. If Jeremiah Bresee born Bef. 04 Jul 1779 was the father of Harmon Bresee born 21 Dec 1788, Jeremiah would have become a father at about nine years of age. I contend that this is not likely. The question them becomes "Who was Harmon's father?".
Based on the timing, locations, and history, I believe Harmon (Hermanus) was a brother to Jeremiah Bresee, a child of John C Bresee and Elizabeth Rossman. As to the Rev. Bostwick's baptism record, I see two possibilities. The naming of the spouse of John Burzee as 'Mary' may simply have been an error in Rev. Bostwick's records, or the full name of the spouse of John C Bresee may have been 'Mary Elizabeth Rossman', ' Elizabeth Maria Rossman', or some such, resulting in her being identified as 'Mary' in the record. In any event, there was no John Bresee with a spouse named 'Mary' having children in that time period or locale that I have been able to find.
By the way, the introduction of the given name 'Harmon' into the Bresee lines seems to have come from the Rossman line. Harmon's mother was baptized as 'Lisabeth Rosman', baptized 12 Dec 1756, Linlithgo Reformed Church, Livingston, Columbia, NY, # 0506, daughter of Jury Rosman and Helena Lescher. A brother of Elizabeth Rossman was baptized as Harmannus Rosman, baptized 01 Feb 1755, Linlithgo Reformed Church, Livingston, Columbia, NY, # 0430, parents Jurie Rosman and Lena Lesjer.
I believe Harmon (Hermanus) Burzee was named for his uncle, Harmannus Rosman, his mother's brother.