It would seem to me to be highly likely that what you have is correct, but, as you say, it would be nice to be sure!
Purchasing the marriage certificate for your Richard and Elizabeth GRAY may help, as it should give you the name of Richard's father.
Re the Special Licence - JM will know more about this in NSW than I do.
Death certificates are often incorrect as the informant is often a generation younger and is thus not acquainted with the parents of the deceased, nor of the early life of the deceased, so the record showing his father as Richard may well be incorrect, or it may have been his second name.
I am assuming that, as you already have names for the parents of Richard W LUDLOW that you also have a baptism and the 1841 census entry for them? If not I'm happy to post them for you.
Too many Richards and Williams in different order makes it confusing!
Judith