Hi Liz,
The following Thomas DOVER, died on Friday 20 March 1874. No death or funeral notices for him in the SMH, on Sat 21 March, and Mon 23 March.
7676/1874 DOVER THOMAS AGE 40 YEARS DIED GLADESVILLE RYDE
Maybe, his parents names will not be on the death certificate, as they are not shown in his death registration, above.
Regarding the MAY family, try Trove search words:
"thomas may esq"
He had lots of daughters. No marriage notice in the papers though, for Eliza R. MAY to Thomas DOVER in 1868.
Mary