Jane is the more common form of the name in Ireland than Jean or perhaps her birth was registered originally with another Christian name or even without a name having been chosen.
This did cross my mind - whether Jane/Jean could have been used interchangeably, or could have caused confusion when registering i.e. could have been registered Jane although the parents chose the name Jean (I've heard many tales of new fathers wondering off to register their children and spelling names wrong and all sorts!

) This didn't seem to bring anything up at my initial search, but something I should definitely revisit with fresh eyes.
Even if you had all the paper evidence by your writings and family gossip it sounds very much like she was the daughter of the what were thought if as one of her siblings.
I'm glad you agree with my hunch! Having discovered that her assumed 'father' passed well before her birth, thanks to @heywood, this seems even more likely. I also remember Jean to be an avid Watford City Football Club fan (UK) and it seemed no-one knew why our typical elderly Irish relative was so passionate about the club. So I went out on a limb and even checked Watford, and Hertfordshire more generally for any "Jean"s born 1928, but nothing.
Margaret’s marriage
https://civilrecords.irishgenealogy.ie/churchrecords/images/marriage_returns/marriages_1938/08889/5215054.pdf
Ah! I found Eileen's marriage cert but not Margaret's! Yes it definitely seems that St. Agatha's could have been the family church, as we know at least two of the sisters married there.
Annie married a Joe Herron, but I don't know when. I wonder if they were married there, too.
You could try contacting the church to check for a baptism record. Responses vary but you never know. Both Margaret and Eileen married at St Agatha’s.
I have read of people contacting churches but was unsure if inquiries like this are usual practise/is well received from churches...but if it is a "done" thing, then I don't suppose there's much harm in a polite request!