I haven't read that Wiki article but everything you quote from it was already in the NZ Folksong page ten years ago.

There seems to be no record of the Irish before the 20th century. A widely sung hymn of popular origin should have left some trace if it was much older.

I want to see that Croatian link resolved. The sound of a Dalmatian klapa is so much like that of a Maori concert party choir it would make a lot of sense for songs to be exchanged between them. (Do those Maori choirs still exist?)