Hi Mare,
Read all the posts thoroughly this morning. You've all been so busy!!
Jumped on IGI last night to see if I could find anything for Will Rob's birth. I found one record:

William Cook
Christened: 26 Nov 1865, Saint Mary, Harmondsworth, London
Father: Amos Cook
Mother: Charlotte
What do you think? Looks likely?
Might also shed light on shipping lists? Will have a hunt and see what turns up.
Name changes are a common occurence. Abraham was often known as Robert, and both Walter Roberts were always known as Bob. Anna Maria is recorded as Maria in later census records. William Richard was known as Uncle Dick. Ellen was known as Nellie, Frances as Fanny, etc. 'Aner' and 'Amos' seem to be interchangeable in all the records so far. Would explain why no records here. Reference to 'Brighton' on marriage cert a possible problem, but as I think you said at some point, info is only as good as the informant...??