Patsy:
As you already discovered RC records for Baslick/Ogulla parish start in 1864, the same year civil registration started.
There is a Patrick Beirne shown in Ballyglass townland in the 1855 Griffiths Valuation head of household listing for Baslick civil parish.
https://www.failteromhat.com/griffiths/roscommon/baslick.php
I did not find a good lead for a civil death record for Patrick 1864 on so I'm wondering if he also died pre-1864.
There is a Baslick graveyard on Findagrave.com https://www.findagrave.com/cemetery/2517269/baslick-graveyard I did not see any record for Patrick or Hanora. I think it would be unlikely to find a headstone for someone who died in the 1850s unless a child or grandchild erected the headstone many years after the death.
Have you considered DNA testing?
Roger McDonnell