I also think it might be worth checking with Prospect Cemetery to see if they have any more information about the William who died on Jan 11 1939 and is buried there.
RK
As RK suggested, you might try writing to Mount Pleasant Group, asking if they would be able to provide any information about Mr. James' plot (also asking if there would be a fee for any services provided).
http://www.mountpleasantgroup.com/deathoccurred/cemeteries/locations/pYears ago, when trying to find where all of my ancestors were buried, most of the cemetery offices were able to help me locate their plots and even provided birthplaces and dates for my ancestors. [In my letters, I stated how I was related to each person. Some cemeteries will not release information to non-family members. I also explained that I was unable to visit the cemeteries as I did not live in Canada at the time.]
Looking at the findagrave website (keeping in mind that a lot of cemeteries have not yet been fully photographed), there are only three William James' passing away in 1939 listed in Canada. Knowing that your William's sister was buried in Prospect, it seems quite possible that William was buried there as well which brings us back to the burial that RK found, for a William James, died January 11, 1939.
I've not yet found an obituary for Mr. James.