
Lack of documentation on ships' manifests was not just for those children who 'came free' accompanying Mum under a sentence 'beyond the seas'.
Even if a family was coming of their own accord, it seems to me that those children in steerage were often not well documented by name, even into early 20th century. There was no real need for the children to be named individually on those voyages, and of course, very little need for individuals to have a portfolio of ID style documents anyway .... During the voyage the numbers were needed for catering etc, and of course any list even if it only mentioned Mr & Mrs SURNAME and x children would be 'too much info' if the steward in charge of allocating mess etc was not literate. The Convict Indents of course are prison records, and so there's more chance of details on female convict records than on any other 'came free' female from first settlement through to around WWI.
I think you have achieved great success in following up on the Col Sec correspondence. PS cannot be Rafferty's rules if there's consistency in birthdays, afterall Murphy's Law says that Rafferty was an optimist.
JM