I notice on the 1851 census that Wm and Thos were both said to be born in Macclesfield rather than Gawsworth. Isn't that odd? I had imagined John Green living on the same farm for some years and one would expect he had been in the same place since his first marriage.
(were his parents farmers? When did they die? UPDATE - Oh, is that John's father being buried in 1838?)
I suppose if John and your ggg-gm were living elsewhere then the children might have been baptised in her home parish, which might be anywhere. I noticed there are no appropriate burials in Gawsworth 1836-1841.
I see in 1861 Thomas and Wm don't know they weren't b in Gawsworth (if they weren't!)
I realise you will have gone over all this a zillion times already, so I'm not sure why I'm commenting! lol