The web site for the PANB is:https://archives.gnb.ca/Archives/?culture=en-CA
It takes some getting used to. The county guides are a good start. Contact information is on the home page.
McMaster University is precisely the sort of place that would be involved in interlibrary loan assuming that such a service still exists.
"The Archives participates in the interlibrary loan system. A substantial portion of the holdings has been microfilmed, and a researcher may borrow up to three reels of film at one time through a cooperating library. References to microfilmed sources will be supplied on request."
Consult with the librarian and also ascertain that the have microfilm readers. If the newspaper for the period you require is on microfilm I thinks the odds are pretty good that you can look at it. Just remember that obituaries might be a day or three after the death.