I don't know if you have checked out Griffiths, but it gives 2 Harrigans and 3 Herrigans in Mayo in mid 19th cent, in addition the 1901 census has some
That would give you the parish, and you could then do some local work by contacting priest or local historian in that area.
If you want to go the whole hog you get dna tests done from male Aus Harrigan and compare with any Irish Harrigans that you can get to do the test (it is possible, I have done this with my own family, including tracing descendants of a convict in Australia)
I agree with this post that we know nothing for sure until DNA testing is done. Birth and marriage certificates may say one thing but does not prove 100% heritage of a certain ancestor...so Susannah cannot be ruled out as an adopted daughter of James and Elizabeth Ruse....
I have read the piece by Bill Jocelyn and it's an excellent article based on some facts via certification and based on what has been written in old newspapers, diaries, etc, all places we go for when we are trying to compile a story of someone who is no longer with us and can't be asked or had nothing definitive from them left behind for us to use.
With family history, it's called looking outside the box reasonably and realising that yes children were born out of wedlock a lot in the early colonisation of NSW. It happens but as NSW colonised more and more, it became a shame to do so like it was in England...there was no one to really judge you in early NSW...the colony was mostly made up of convicts, and upper class noisy snoities came later...
Sorry just my honest opinion...