Since you have done so much already but without success, it would appear that you might have to fall back on the old-fashioned method of going through the Parish records.
The Family History Library Catalog has:
Archdeacons transcripts, 1725-1812 Parish Church of Little Brandon (Norfolk) (Main Author) Baptisms and burials 1726-1731, 1764-1812 Marriages 1727-1731, 1764-1811 - FHL BRITISH Film [ 1526810 Item 15 ]
If you have a LDS Family History Library within reach, the idea would be to order the film, book a viewer upon its arrival (usually within a few weeks) and then work your way through the records. Somewhere in there you will find the record of Jonathan's baptism and the names of his proud parents. And while you're at it, have a peep at the marriages as well - the parents' wedding should also be recorded. There are heaps of possibilities - it can be fascinating!
However - if you've already done all that, then: sorry, I've no other suggestions!