Hi Lucy2,
Thanks so much for doing all that investigation. It would have been a lot easier to find a Birchall born in Tasmania as there are many there including the book store chain of Birchall.
I also found the Louis Edwin's in Tasmania you mentioned and searched their family trees a bit but they were both false leads. I also found a Marian Sutherland b 1847 who arrived with her parents Betty and Andrew and siblings in Geelong, Victoria 17 Jun 1854 aboard the ship Conway (dep Greenock, Scotland). I even added them to my tree for a while as the only potential lead.
And I found a Marion Sutherland via FamilySearch on NZ Immigration Passenger List who arrived Canterbury 13 Oct 1863 having left from Renfrewshire 4 Jul 1863 with parents Hugh and May - a baby probably that year.
I have even searched for British born Birchalls with various mixes - Harold, Charles, Edwin/Edward and Louis/Lewis. I found one born in Christ Church, Spitalfields and wondered whether someone could have turned that into Christchurch NZ.

But his MC uses Canterbury for his birthplace not Christchurch.
His father was stated to be a Government Accountant, would the NZ archives have data on their employees somewhere I have not found?
Harold has proved very frustrating indeed and I tell my husband that his Great Grandfather must have been a con-man and that his name (and my daughter's) is probably not Birchall at all, at all!!!!

Thanks again,
EJB