Good lists of CLEMENT births/baptisms. I can't see the name "Christina" either, at least not on the images I have access to.
I think the lists are fairly complete but have a couple of 'maybes' to add.
I would agree that the Shoreditch CLEMENT family is not relevant to this search. On-line images give their address as Curtain Rd, Shoreditch and the father's occupation as 'Cow keeper' (I think)
James and William CLEMENT, baptised at St Nicholas October 1817, have a father who is a labourer and the address is Flagon Row, Greenwich. Whether this is the same couple who were in Shoreditch till 1814 is unclear, but I think they are also not relevant.
Eliza Ann CLEMENT who was baptised on 24 May 1824 at St Paul's Deptford has, as already mentioned., only her mother's name listed - Mary Ann CLEMENT and has the word 'Base' listed under her name so Mary Ann was unmarried at the time of the birth. Address given is Crossfield Lane. There was another CLEMENT family living in Crossfield Lane - George and Elizabeth who seem to have been baptising children at St Paul's from about 1802. (The first of these baptisms that I see on FreeReg may be the mother of Eliza Ann:
Mary Ann CLEMENTS
Baptised 29 Aug 1802
Father George, Labr
Mother Elizath
Abode Church Street)
I do not see an 1804 birthdate for Eliza Ann - the on-line register image has no year date listed, and FamilySearch lists her birthdate as 1 May, 1824. However, perhaps there is another record.
Now - there is an interchange on various records of the names CLEMENT/CLEMENTS and even CLEMENS
For example, there is this baptism again at St Paul's Deptford:
Mary CLEMENTS
Born: 9 Nov 1814, Baptised: 26 Mar 1815
Parents: William (labourer), Mary
Living at Crossfield Lane
Also William and Mary CLEMENS, living at Baileys Rents? Or Back Lane, Deptford (and later nearer to Greenwich); with children baptised between about 1815 to about 1830. His occupation is consistently 'smith' or 'blacksmith' and occasionally 'balcksmith DY' spoo he was also working at the Dockyard at the same time as Charlotte's father.
Obviously sorting out marriages and census entries with so many similar names won't be easy!
At least the children of the Victory Street couple seem to have more than one forename in most instances. I still have some difficulty with the births of Charlotte and George Bingle being so close together. I think it's possible that the on-line images are not necessarily the original registers but contemporary copies (bishop's transcripts?) However they are labelled as "Parish registers". It may be worth contacting FamilySearch and see if their films are available to view as these may be from the originals. I could be entirely wrong with this, though.
Now, to be mischievous I am adding this child to the mix which will add to confusion when seeking MD or census records. I can't readily see any thing for her..............
St Anne's Soho,
Clementina CLEMENTS
Born 6 May 1821, baptised 5 May 1822
Parents: John (occ tailor), Elizabeth
Abode: St Martins
Sorry, such a long post. Judith