Did RHS emigrate to Australia? (as you say he travelled to England several times)
If so, do you know when he came to Australia and who with?
Do you have him on any English census, with or without mother, siblings or family?
It seems a little odd that he does not know the maiden name of his own mother. If he was illegitimate he may have been registered with her surname and later took the surname Smith if his mother married for example.
He gave the information about her on his own marriage certificate and said her name was Anne. What was the other document which named her as Mary?
Do you know what happened to Anne?
Did RHS die in Australia? Sometimes information on d/cs is not correct, especially relating to parents of the deceased.
I understand you are trying to confirm the story, but I think some of your 'evidence' is perhaps a bit 'weak' for want of a better term (sorry) eg the names he gives his children.
This is not proof that CLB
is his father, but only that he
believes CLB is his father.
Like brigidmac, I am curious about the middle name of Hastings, and wonder if that is a clue to his mother's surname or .... if it has some other relevance? (some middle names end up being red herrings ... some not)
If you can locate living descendants of CLB and persuade them to take a DNA test I think that might give you some answers.