After discussing with another lady also researching Ardle McKenna, she suggested the possibility that Ardle travelled between Scotland and Ireland for work which may explain why his children were born in Scotland but an Ardle McKenna appears in the right place in Ireland in the Griffiths valuation.
I spoke with my Dad about this and he said that his father and brothers were taken to Ireland to work at least once that he knew of, by his grandfather (Ardle's son), so there must have been an ongoing connection.
So just wondering if Ardle appeared in the Scotland censuses/baptismal records but also managed to get himself on the Griffiths valuation by travelling back and forth for work. The other researcher could not find the family on the 1851 Scotland census even though one of the children had been born in Scotland by then.
In one of the Scotland censuses Ardle was down as living in Nob Row, a place in the town where workers who replaced striking workers were housed, implying he was a migrant worker for a time before settling there. I don't know, it's all speculation!