Seems we have a mystery here! There is a Peter Jenneson (sic) in the 1790 US Census living in Charlton, Worcester, MA. His family is a pretty good fit for Peter & Mehitable. I looked on Ancestry and NEHGS but found no birth records for Charlton. Not every community in MA is included in the pre-1850 MAVR (the "Tan Books"). If Charlton is one of the communities not included in the Tan Books that could be the source of our problem. I'm considering hiring a NEGHS researcher to do some local digging.
Purley purchased several tracts of land through the government's cash sale program so last week I requested the file for the first of these purchases. It's a long shot but maybe this will provide another clue to his birth.
I'll keep you posted.