As Jemimas Mother was a Jemima could the only daughter I can find born to William and Jemima be a hint.
Elizabeth SWETMAN, Baptised 05 April 1795, Heigham, Norfolk (Freereg)
Have you looked outside of Norfolk for his christening?
Just because he married and had children in Heigham does not mean he was born there.
I feel for you as it is a difficult one.
I still think the death junev found is a possibility. People did move areas and the age is abt right. Often older parents lived with their children.