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It seems unlikely that someone like Joseph would be sent by a mill owner to Australia to negotiate buying wool. If he was doing that he would have described his occupation on the marriage record in different terms.
A timeline shows his working activities:
1851 Census - Wool sorter
1860 Marriage - Wool sorter
1879 Mentioned in the Police Gazette as the victim of a robbery - Wool sorter
There are also mentions in trade directories of 1875 and 1876 of him being a draper. So it appears he was working in different aspects of the wool industry.
In 1882 Joseph is listed in a trade directory as a wool broker and by 1884 a wool merchant. He may have been doing this before that date but by then he was spending enough time at it for it to be considered his main occupation.
Joseph was obviously ambitious and saw his future to be in the colonies rather than be held back be lack of education and opportunity. It seems he worked hard, was interested in his local community, church and politics.
If you have not already found this - there is some information about Joseph here. This blog has transcripts from old newspapers and other historic material.
https://macdonaldtownbicycleclub.com/2015/11/30/pulpits-and-personalities-the-shifting-sands-of-time-holy-trinity-church-erskineville/Even John Sutcliffe Horsfall who went to NSW in 1856 at the age of 19 was employed as a clerk even though his family were wool manufacturers in Bradford. He had to work his way up to become a partner. Read about him here.
http://oa.anu.edu.au/obituary/horsfall-john-sutcliffe-508I don't think the 2nd Lord Carrington had any engagement in trade. His own father, upon being elevated to the peerage, was required to give up his work in the bank by no less a person than King George himself. Family money or land owning was the only acceptable source of income at that time.
The 3rd Lord Carrington did not arrive in Australia until the second half of the 1880s after his brother Charles was appointed Governor of New South Wales in 1885. Joseph Horsfall died an untimely death in 1885.
I think your family story may have got mixed up with the John Horsfall - Lord Rupert Carrington connection. It seems that John S. Horsfall was well known as a wool trader and grazier. Joseph may have had some business dealings with him.
I think it would be quite hard to find out if Joseph lost any wool on a ship as his wool would probably be only a part of the cargo and the bills of lading may not have survived. Mention of the Cape is interesting as by the mid 1870s the preferred route would be via the Suez Canal. The insurance records would probably be with Lloyds of London if they survived. You should ask about ships' records on a forum devoted to historic shipping if you can find one.
I hope you find this helpful. I have investigated many family stories, in my own family and for others, and so far have only found one that was actually true. Some have a little kernel of truth that has been mis-rembered over the years but most are due to mix ups with people of similar names or similar events, or prevarications to hide uncomfortable facts or even "jokes" by elders taken as gospel by young children.
Sincerely
Venelow
Canada