Can't provide any help but I'm interested in the topic.
My husband is thinking about applying, his grandmother was Irish born.
But - big but - his mum was born a Meagher, and at some point "acquired" a different surname. We think this was because his grandmother was living with another man, and his mum was basically told "you're this name now." None are left alive to ask, and we doubt that Irish authorities would allow this, and instead need documentary proof, of which there's none, to explain the sudden shift in surnames.
I shall follow this thread with interest.