I have just picked up your post whilst searching on line. I am descendant of Richard Greest (b.1805), a blacksmith from Pitt Hill near Hambledon. He had a son John Greest b.1858 who I presume is the father of your John Greest b 1884 Petworth.
A relative (now deceased) carried out this research and found that the Greest's originated from Lurgashall, near to Petworth. The earliest ancestor I have recorded is a Thomas Greest, b. Lurgashall in 1585.