There's a William GARDNER baptised in Banbury which borders Hanwell (Alice's parish) and is about 2-3 parishes over from Deddington.
He was the son of Valentine GARDNER baptised 6 September 1702.
Not saying it's him but a candidate. There may also be others about in the inbetween parishes too.
Eleanor HIRONS who married John WARD came from Hornton which is a couple of parishes over from where they married.