OP - you mention checking Griffith's Valuation for Jeremiah Murphy entries.
But that for Cork dates from 1853. Have you checked the tythe valuations, which are substantially earlier?
Of course, you now have more than one civil parish to deal with.
And Jeremiah tended appear as Jerry or Gerry.
As it happens, Murphy is a very numerous surname, and Jeremiah was a popular Christian name in Cork. So I think there will be quite a few.