How pleased I am to see your reply, which I've just read. I have been researching this family for the last three summers.
Family lore and memory is so interesting - here is what I can throw into the pot, so to speak:
Starting with Joseph McMahon, then. I know much more now of course, but there are still great gaps! Joseph was born in Fintona, Tyrone, Ireland c1803. He was a weaver [the bottom fell out of wages for weavers in the county] so he enlisted in the (British) 63rd Regiment on 1 Jan 1823 - his regimental no. was 373. His regiment served in various parts of Ireland, leaving Ireland to go to Windsor (ENG) between May-June 1826. The regiment then undertook (uneventful) peacekeeping activities in Portugal, which it left to return to England. The regiment was next posted to AUS. Joseph arrived in a detachment per 'Governor Ready' - the second voyage [which is where I got confused and thought he was in the 39th regiment in the first instance]. The ship arrived in Sydney and unloaded its convicts and the military - only recently have I worked this out, and its interesting you think he went to Norfolk Is [will follow this up, thanks:)]. In 1831 he was detached to Macquarie Harbour, and was rotated back there at the end of 1832. At this time Capt. James Briggs was the commandant [note may have been related to Leonard Briggs, Fanny's first husband]. I don't have specifics after this until the unfortunate matter of the fight and the victim's death some days later. [Family lore on this side was that the fight involved the 'honour of the regiment' - hmm..] Joseph was arrested, tried, and 'transported for life' in TAS. He was a rowdy prisoner, as can be read in the TAS records online.
From 1839 he lived in Longford, TAS. In 1843 he applied twice to marry 'Sarah' - and I now think Fanny used these names (Brigg, Reading) because she couldn't prove she was widowed; and, that after she could prove it, she remarried in the Catholic Church. [Does your part of the family have the prayer book you mention?] Alternatively it could have to do with her family's religious background...
Fanny's line is quite fascinating in its own right - another time though. Joseph and Fanny's son was Joseph Charles McMahon - he was very involved in the community, clever and amassed a fortune [see Trove]. He, as you say, was educated at the seminary in Hobart.
The house the family lived in -in Longfort, TAS- was called Fintona - various of my in-laws visited it years ago. Joseph Charles married -three- times. Maureen and her siblings, were the issue of those marriages. Marion, the oldest, was already married (when their father died), but I wondered what happened to the others after the death of the last wife, ie Frances Josephine (Brown) McMahon. The Brown family are the cousins you refer to in Moruya - did Sheila go there too? I believe the son, Joseph Edward, eventually attended uni, did not graduate, married young. You say that Joe attended St Virgil's, Hobart - wonder if they have publically acessible records?
It's said that this generation lived the high life and spent without thought for tomorrow. So all of a sudden, as the ancestry ad says, they each bought a pub.
I am happy to share more - if you wish to conact me at elbe12 at westnet.com.au.