According to the usual sources, Garry Owen na Glora is an alternate chorus. Jim Dixon posted the 'other' Garryowen lyrics above. By my count, that makes twenty (20) variations on the main title… so far.

1792 – The title gets a mention in the Madame Mara incident in Limerick but, so far, the earliest coverage of that doesn't show up in print until 1812, London.

1797 – Corrie Owen?
“A Duett, for two Performers on One Piano Forte, by the most Eminant Composers” Note written on front cover states: “made into duetts by Hook” Also published in London.

1799 – First mention of the title playing in the U.S.A.

1822 – John Banim posts lyrics to the Literary Register, London but earliest mention of them, so far, doesn't show until Crofton-Croker, 1839… London… again.

Kinda thin on Irish sources proper, now that you mention it.