Hi Neville,
Perhaps I have not placed sufficient importance in my previous posts on your threads and on threads that others start regarding the lack extant records for NSW family history in the early years from first settlement to say the NSW 1828 Census. Even that census is likely to have missed many families.
But significantly, in my view, until you have joined the dots from you back to your William SUTTON, you are umm.... basically ... umm.... simply speculating that any of the SUTTON family departing NSW in May 1818 per the David Shaw are your ancestors.
May I assure you that there are many NSW centric family history buffs whose research extends way deeper than online images found of public records held at NSW State Archives. Even those who confine themselves to NSW State Archives delve much deeper than the NSW Col Sec Papers, or the Musters, or the 1828 Census. Then there's the resources at the NSW State Library. Then there's the resources at the NSW City of Sydney Archives. Then there's the resources at the Society of Genealogists.
Have you sought to locate any Family Bibles in your NSW ancestors born in say the 1800s ... the front sections of those often have the Baptism info for the children and grandchildren born of the original owner of that rather large, leather bound book. Do you have copy of private correspondence between NSW family and their cousins/aunts/uncles/grandparents back in Britain, giving news of births, marriages, deaths, employment opportunities, then current addresses ....
In my view, the Macquarie era 1810-1821 and the Bigge 'Royal Commission' were not really interested in recording the personal/identifying/sensitive information for those who arrived in NSW who were NOT under a sentence of a civil court. In my view, there's scant information for those who 'came free' unless they were public figures. In my view, there's little or NO extant public records of perhaps most of the 'came free' females - whether came as babes in arms of their convict mum, or as children of a garrison soldier, or as children of free settlers.
On the other hand, it is of course within your own remit to decide: how you know if you are a descendant of any deceased person; how you share that knowledge; who you share it with; when you share it; why you share it and where you share it. So I am hoping you are not setting aside all the searching you have already done. I am just perhaps being pedantic and hoping that you will consider undertaking 'real research'.
I assure you that there is something very special in being handed a file you have ordered (no charge !) at the NSW Archives, to sit, alone, and then, on working your way through it to come across the actual signatures of your Great Great Great Great Grandfather, and two of his grandchildren on an official document, when you have known, per oral history only, for over fifty years that two of your own given names are for those two grandchildren. That's research - not a fluke, not a tip from an online index or image, but solid research through deeds, private family papers, Mitchell Library, State Library, SAG, talking with ancient living rellies, reading my own notes from the 1960s and then ..... - finally confidentially 'knowing' which document that chap and his two grandchildren MAY have signed as witnesses to a possible incident in the lives of their then neighbours and that those neighbours DID take legal action against the perpetrator who may have been a 'jolly jumbuck'.
I cannot confirm or contradict your thesis that William SUTTON per the David Shaw ex Sydney 1818 was the grandfather of Harriet, or that Harriet's mother was William's daughter or that that daughter was the mother of Philip MURPHY who died aged 29 .... but I can say 'Persist, keep searching, start researching - the thrill of the chase etc.
Look deeper to see if there is proof that you have definitely found all the SUTTON residents in NSW in the Macquarie era. Join all the dots - carefully, accurately and then smile. JM