Julie, I'm sure there is a south Lincolnshire link here somewhere, because both Pitchers and Cropleys are well-known south Lincolnshire farming families, and it would not surprise me if Job Pitcher & Ann Cropley came from around Boston.
The Pitchers are my relations - eg. George Pitcher born 1844 in Spalding, Lincolnshire who had 10 children in the Wrangle area of South Lincolnshire (about 10 miles from Boston).
I don't know George's siblings but it is very possible that one of these married a Cropley. I haven't been researching the Cropleys, but they crop up quite a lot in Lincolnshire press cuttings - for instance I know that Mr & Mrs F.L. Cropley (big in local farming) lived at The Chestnuts, Swineshead (another village near Boston), and their daughter was married in 1959 to another local farmer called Hardy. So they must have been born around 1910-1920 or so. Maybe this will help?
One of George's sons was William Pitcher (not sure of his middle name) but I don't know whether this will be the William Arthur you are looking for. He was born in 1881 in Wrangle, Lincs, and he married a Mary, and may have moved later to South Africa. He died in 1955 aged 74.
If I can be of any further help, please let me know.