I'm new to this Forum and did not even know that it existed!
I too have APPLEGATES in this area and descend from Thomas A and his wife Ann DURRANT who were md. in 1785 at Ludham).
Their seven children included Ann (c.1786 Ludham), George (c.1788 Ludham), Richard (c.1790 Potter Heigham), Henry (c.1793 PH), William (c.1794 PH), Mary (c.1797 PH) and Charlotte (c.1799 PH). My ancestor is Wm who md. Eliz ALDRIDGE (of Hickling) in 1825 at PH, having 14 children (all born at PH). Their third daughter Mary Ann (c.1832) md. Robert BULLEY at Catfield in 1852 with 12 offspring incl. my g/father Edward Christopher B (b.1865).
Ted B (as he was known) emigrated here to AUS in 1889 and md. my g/mother Elizabeth HOWLETT (aka COFFISON) in 1900 at Charters Towers, a goldmining town in country Queensland, where my mother, Blanche (the youngest of 10 BULLEYs!) was born in 1920.
I wondered if your William A and mine may have been the same person as he md. a girl from Hickling... Otherwise, if anybody else out there has any connection with this line, I'd love to hear from them.