Yes my G/father was TEC and yes Eric did connect the family with Martha Gelling and Robert Corkill. I went back up the tree to Thomas C and Catherine Clague and am trying to follow their Children, this is where J T Corkill and Eliz Craine came into it JT bc 17/5/1795, married 2/11/1816 to Eliz Craine(my interpretation)? From them I agree with your list of children but the marriage of their child John c15 Oct 1819 is the link in doubt with Mary Ann Brew
The children of Thomas Corkill and cath Clague have raised problems in other trees where I have been contacted as a relative but the data has been erronious getting proof is the hard part from NZ and this message board has been an immense help