Someone uploaded some scanned pages for church records for Readington Church in New York (https://www.familysearch.org/tree/person/memories/KFQK-YRW)--very helpful and nice to see sources!
A question was sent to me whether this the same John Simonson who fought in the Revolutionary War and was a lieutenant, who later moved to New Brunswick. I do not think so since according to this source (source...), the death dates (1804 vs. 1816) and names of family members are different.
That does not rule out that John Simonson (1743-1804) did not fight in the Revolutionary War. See for example this book, that to me implies there might have been two ensigns by the name of John Simonson (any opinions?). Of course, I am still not aware of any definite Revolutionary War service: https://books.google.com/books?id=v5k_AAAAYAAJ&pg=PA9&lpg=PA9&dq=John+Simonson+and+the+revolutionary+war&source=bl&ots=BIB-eRhyae&sig=ACfU3U0eHp397G6jL4sjy6AGOU9VBt29sA&hl=en&sa=X&ved=2ahUKEwizmLmxtonlAhVB7J4KHYRsA-0Q6AEwA3oECAkQAQ#v=onepage&q=John%20Simonson%20and%20the%20revolutionary%20war&f=false
