I am thinking that St Mary the Virgin Eccles is quite a long walk from Clifton. Though I am not on the spot to know precisely the geography nor the customs of the parishioners.
Clifton is in the ecclesiastical parish of Eccles. All of the other children, including Thomas, were baptized at St Saviour's, Ringley, probably because it was nearer or maybe even because there is a plaque in the old chapel that states, "This Chappell was erected at ye cost and charges of Nathan Walworthe, son to Elis Walworthe, Ano Do 1625".
There are several Nathan's baptizing children, even in Ringley, at this time.
As you mention there is an Ellen, dau of Nathan, buried 5 months, in 1830 at St Mary the Virgin, but there is also a Rebecca, dau of Nathan, buried 2 years, in 1835 at St Mary the Virgin.
True I still have some unanswered questions. I have not found the burial of the first wife who was called Elizabeth and/or Betty. There is certainly time to fit in another child, or two, after Thomas - between the birth of Thomas in 1828 and the remarriage of Nathan in 1833.
This is all not to say, however, that for some reason they had to bury a little Ellen at St Mary the Virgin. As you mention a baptism would be helpful.
