Since William Harrison married Sarah Bennet in NYC in 1780 and the daughter, Sarah, is said to have been born in Nova Scotia in that year, it doesn't seem to fit with Howe's trip of 1776 from Boston. I think there was a Southern loyalist named William Harrison, but I don't think its my guy. There is, also, the famous Harrison family (2 presidents) from Virginia but this is not mine either. Its a pretty common name, which makes things more difficult.
50 is a big birthday. I already passed through it to my current 56. Good luck with your researches and keep me advised, especially, if there is anything I can do to help here in Westchester.