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The RC records for Howth start in 1784 https://registers.nli.ie/parishes/0662 I checked the subscription site Roots Ireland for records in North Dublin including Howth and the earliest Stephen Griffin baptismal record on Roots was in 1833. Likely your Stephen was born in a parish before records are available. There are Griffin baptismal records in Howth in 1785 (Anne) 1786 (Thomas) 1786 (Michael) Rose (1788) John (1789) Possibly some of these Griffins are related to Stephen.
You may want to post Stephen's story to our XO Chronicles site and possibly someone will see a connection. https://www.irelandxo.com/ireland-xo/history-and-genealogy/ancestor-data...
Have you considered DNA testing?