Thanks Trish.
It's mostly about a process of elimination now, as I've tracked my 4x great grandfather, George back to his baptism at St. Mary and St. Cuthbert,.Chester Le Street, Co. Durham, on 22nd March 1761. This parish record shows his father as 'Geo. Snowball, of Birtley, Husbandman and Mary, his wife'.
George Jnr. lived at Harlow Hill and was buried in Ovingham, so they all seem fairly localised.
I'm now trying to find George of Birtley and Mary. There are not that many, except for George and Mary Robson who married inn Long Newton, Co. Durham 30th Nov 1758 but it seems a long shot, given the distance from all the action. Allendale seemed a bit closer but, as you've discovered, he's not my man.