Re. the text being very stable (I agree, incidentally!), there is one other verse which I've seen in several printed sources - all of these being of the popular "50 best Irish Songs" variety - which seems a later interpolation intended to localise the song in a particular time, though in a place rather remote from Armagh:

"When I was a young lad, King Jamie did flourish;
With my harp owre my shoulder I followed the war:
I was known in every glenside from Wexford to Durris
As the bould Phelim Brady, the Bard of Armagh."