Welcome to Rootschat
Virtually all of Beds pre 1812 has been extracted onto the IGI, so if it's not on the IGI then the parish register is unlikely to add much. But have you checked the parish register for the marriage entry to see if his parish of residence is quoted, and to see if any helpful witness names might be there?
If all his children were born in Northants then it suggests that is where he may have been from. There's a member submission on the IGI (to be taken with large pinches of salt) of the christening of a James Gooding on 9 Aug 1767 at Ecton Northants, which is only 3 miles from Moulton.
Regards
David