However, the father of that Ellen Hamilton was Charles Hamilton, and she was born in 1845.
The Ellen Hamilton that I am looking for had a father who was John Hamilton, and info from Censuses seem to place her with an 1847 Birth.
Actually,
- not:
had a father who was John Hamilton --
stated that her father was John Hamilton on one document, her marriage certificate
- your Ellen gave census information that would place her birth in the period from April 1846 to March 1847 (and someone else entirely gave death cert info amounting to a nice round number if nothing else, but matching what was at least Ellen's belief about her age) -- late 1846 is only one year out from late 1845
A statement of father's name on a marriage certificate is not proof, or even very good evidence, of father's name. What does match, in this case, is the father's occupation.
An age variation of one year between recorded birth and census age, for someone born before 1850, is hardly even a pebble on the path when it comes to obstacles.
My grandfather was born in 1901. Until he retired, he believed he was born in 1900 -- his mother died when he was 10 and he spent the rest of his childhood moving among the homes of older siblings. He also had his own name entirely wrong. And his father had invented a name for himself 20 years earlier, and a named a fictitious father on his marriage certificate to go with.
Looking for perfect consistency in mid-19th century records could be a futile effort.
That's not to say this Ellen is your Ellen. It's just to say that your problems with the evidence might be overstated.

I gues the big question is whther that Deptford Ellen can be ruled out by finding her with a separate existence concurrent with your Ellen (or death, emigration ...). So far, there doesn't seem to be a separate existence for your Ellen before she married, at least. Is there one for the Deptford Ellen after your Ellen's marriage?
(That was how I determined the identity of my gr-grfather: two identical people with different surnames, one existing in records only up to 1873, the other springing into existence in 1881.)
Of course, the problem with that process is that absence of evidence is not evidence of absence.
