I have that Harry Beanham photo of the 350 GCS, too. It's the only photo I have of a B&S engined bike in Oz, other than Ever Onward, of course. And New Onward.
Two 350cc B&S came to Melbourne. One went to Mairs, ironmongers who became the McEwan hardware empire, the other went with two 500's and a V twin 1,000cc to consignee unknown, but Stillwells must be a good chance. Norm Maplestone bought two V twins, but there's no record of him building a bike out of them. If he had done, it would have been reported. A B&S V twin cycle car emerged in Surrey Hills (Melb) in 1928, then vanished, but that would have to be one of Maplestone's engines. Norm McCubbin reportedly had a V twin B&S as a mantel-piece ornament, which one I don't know. His wife finally protested, and it went to Moorabbin tip in 1965. Despite extensive excavations by Warren, it's probably still there.
In Sydney, P&R Williams bought a 350 and a V twin 1,000cc, but there are no reports that I have found of a B&S Waratah.... A second Sydney shipment was a 500 and a V twin 1,000cc. The 500 found it's way to Wilcannia, and thence Ever Onward. No record of the twin.
A load of 350's went to Perth. All the loose engines went to the WARailways. Stotts in Fremantle moved a number of 350 B&S engined Coventry Bicycles machines, but they were imported as complete machines. Registration records suggest at least a dozen were on the roads over there. They were registered as "B&S", or "Coventry B&S".
All jigsaw pieces gratefully accepted......
JFerg