I have great news! I found the obituary record for my great-great-great-grandfather, Bernard May, from the Youngstown Vindicator on page 3 of the November 29, 1904 issue. https://news.google.com/newspapers?nid=pqgf-8x9CmQC&dat=19041129&printsec=frontpage&hl=en
Unfortunately, it does not mention his parents' names but it does mention the names of his children leading to believe that Bernard and Joseph were both dead by this time. However this is simply a hunch as the article lists out every child by name in birth order except for Mary who is listed as Mrs. John Loftus as she was already married by this time. The lack of Bernard, Joseph and the original Michael from this list suggests they are dead at this point. Especially, since they don't mention Bridget as she had died 13 years before.
Does this make sense?