Bert - I contacted my 5th cousin, Peter Michael, and his comment was:
The Peter Michael who seems to fit a birth year of 1808 is a grandson of Andrew I through Andrew's son, Adam (10/14/1766-?).However, this Peter does not show as having married a Phoebe Simpson.He married Delila Hilton and then Patsey Hilton. My guess is that the Peter Michael you are looking at is descended from one of Andrew's brothers; Christopher, William, or Nicholas.
I imagine there is a connection, if only we can get your Peter back one more generation!