Since a united Ireland wouldn't have the Queen, God Save the Queen would be pretty irrelevant. The Sash has a better tune anyway, and I can quite imagine some arrangement that would include it alongside the Soldier's Song. Or maybe Lilliburlero, though that might be confusing for listeners to the BBC World Service.

After all, that's more or less what what they did in the new South Africa, where the anthem includes both Sikelel' i Afrika and the Afrikaans Die Stem.

I think something that represented both traditions alongside each other would make more sense than some cobbled up novelty that didn't have any roots.