Hello lovely to hear from a distant relative. I don't know where William Conway came from the only information I found out about him was that he was a first mate. I found the following article through the Trove web site, you may already have this of course.
THE WESTERN AUSTRALIAN JOURNAL - SATURDAY, DECEMBER l8, 1847.
During the time the Champion was lying at the Sound, a melancholy accident happened, by which the lives of the mate, Mr Conway Baine and Kaine, two seamen, and a native lost their lives on the 2nd inst. It appears that during the absence of the party who went to Cape Riche, and who were accompanied by Lieut. Helpman, a native prisoner, suffering from disease, was sent on board by the Resident, for the purpose of trying the effect of change of air; his moaning however proved such a constant annoyance to the crew, that it was determined to take him on shore again; for this purpose Mr. Conway and the two men started from the vessel with him, but had not proceeded far before a sudden squall came on, and the sheet being it is supposed, fastened, the boat was swamped, drowning all on board, who were with one exception, good swimmers, yet were not seen to struggle, excepting Kaine who was shortly after picked up insensible, but all the efforts of Mr Wight for his restoration proved unavailing. The other bodies were not found for some days, when Lieut. Helpman fired a gun over the spot and from the concussion, the bodies rose to the surface about two hours afterwards. Mr Conway was much respected and had been mate of the vessel for five years; he has left a widow and one child, for whose benefit a subscription was generously and promptly raised by the residents at the Sound, amounting to £56; a subcription paper is also being handed about Perth and Fremantle, which we hope to find will meet with good success from the charitable feeling of our settlers.
There is a longer version of this article on the Trove web site if you are interested.
I hope this helps
Liz