I think I have found him.
I got an email from a lovely lady at Cornwall Legacy, who made me think I should be looking for a separate established church baptism, in addition to the Wesleyan (she was unable to find the Wesleyan baptism) as it was often a condition of being married in the established church. So... with that in mind, I took another look at the immigration application which stated that William Bawden was 39 in April 1838. This meant that I was looking for baptisms after April of 1799,
separate to the listed 5 April 1800, The only one that came up in cornwall which I hadn't previously ruled out (because of census data etc) was a William Bowden son of William and Alice, in June 1799, at Mylor. Looking further I saw that they had two daughters (one died within the first year) both spelt Bawden.
Mylor just happens to be where Trefusis manor once stood, Trefusis being the name of numerous early family properties in Australia, as well as the middle name for about 8 descendants.
As William and Alice Bawden of Mylor do not show up in the census at Mylor in 1841 I can be fairly confident that they did move. Other William & Alices in the 41 census have been ruled out as being the same ones from Mylor. Maybe Alice died early (fairly likely with only 3 children?) I know that absence of evidence is not evidence of absence, but....
So I am pretty happy with this result, it fits well.
Thanks for all of your help Osprey
