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Just posting this as a ref:, it may or maynot be the correct 1871 census re opening post

Smiths Court, Manchester, Lancashire, England

John   Smith   -   -   Male   30   1841   Hawker   Ireland
Mary   Smith   -   -   Female   28   1843   -   Ireland
Mary Jane   Smith   Daughter   -   Female   1   1870   -   Manchester, Lancashire, England
Michael   Smith   Brother   -   Male   13   1858   Hawker   Manchester, Lancashire, England

Probably NOT our man
SS

England and Wales Select Cemetery registers   Ancestry
NameJohn Smith
Age28 Record Type Burial Birth Date abt 1844
Death Dateabt 1872 Burial Date31 Jan 1872

Philips Park CemeteryCemetery SectionEGrave Number455
Occupation Hawker

It be nice if there was more information.
So agreed , probably not the one we are looking for .
They were on the same census district as the Rev Gornall in 1871. Another dead end. 

I think this is the man who was at the baptisms J Gornall.
Piece 4033 Folio33 Page number22

1871 Ancoats Manchester
Rev John Gornall b 1824 Preston
Occupation  Catholic priest of St Albans.

Are the Smiths in the same area. 

Civil marriage
MCANDRYJames
BYRNEHonora1879
Manchester Register Office or Registrar AttendedArchives+,
Manchester Central LibraryMCR_RM/97/104
Lancashire FreeBmd

The inquest is in Manchester Times 12 March 1881.
John Smith was of Worsley Street Deansgate.

 you say have Mary Jane census after her marriage to James Cain.
I'm not finding one for certain
It would hopefully have where she was born.
None of the baptisms found have an abode which is not helping.