Hi David
Don;t want to be too critical , but it would have been good to know of the change of name before looking for Radcliffes. However based on that information , the obvious reason for name change would be that he jumped ship and would have been sought after as a deserter.
There was no census in Sydney in 1854 or any year since ( at least published.) The only census in NSW was 1841 and this only gives the Head of the house.
There were two marriages of a James Parker in 1857 , but I have established he married Bridget Regan . They had had ten children from 1858 to 1871 , sadly they had 5 children die as babys including twins Esther and Benjamin in 1867 , their daughter Catherine died in 1883 aged 25.
From the Trove site - free - NLA - Newpapers searching for "Parker , Isle of Man ;
Sydney Morning Herald 30/4/1915 - Silver Weddings :
Poole - Parker , April 30, 1890 at St Saviours Church, Redfern , by the Rev A G Stoddart , Harry A E , eldest son of the late G H Poole , Bristol , England , to Louie , youngest (surviving) daughter of the late James Radcliffe Parker of the Isle of Man. Present Address Mona, Alfred St, Coogee Bay. ( Daughter Louisa born 1870)
This led to :
S.M.H. 30/10/1893 :
4 Funeral notices for the death of Bridget , from husband James , sons Edward and James Henry , Mr & Mrs Poole , and Mrs Sidney Burgess (Eliza). the funeral left her address 40 Chisholm St , Moore Park , Sydney.
Which led to :
S.M.H. 1/11/1894 - three funeral notices , this one form the two living sons :
The friends of Messrs Edward and James Henry Parker are respectfully invited to attend the Funeral of their late dearly beloved Father Mr James Parker to leave 192 Castlereagh St, City , this morning at 8.30 for Waverley Cemetery . H Mason, Undertaker, 223 Oxford Street , Darlinghurst.
Both James and Bridget's death registrations show parents unknown.
Bridget's 7988/1893
James 1435/1894 ???
The 1435/1894 is the only registration for a James Parker in 1894 , but the number 1435 indicates early in the year , not November.
Cheers
David