That makes sense. Thanks for your detailed reply. It's difficult to use Google to find examples of these in print because you can't tell it to look for genitive case obviously
The best I was able to do was find an example of "na n-aon bhliain déag" on an Irish website, apparently treating this as any other plural genitive, which is semi consistent at least with the way that adjectives are declined after the "teens" (which is to say it's the plural lenited form - i.e. aon bhád mór vs. trí bhád mhóra.) whereas, as you say, the other non-déag compound numbers are treated as their base number plus the larger component, i.e. aon bhád mór is fiche. What you are reporting about it being "an aon fhuinneog déag" is consistent with at least one comprehensive document I found (Mechura's "Uimhreacha") which does contain some obvious errors but appears to mostly be thorough. I had doubts about it precisely because of some of the errors I found in his document though.
My confusion partially stems from the differences among sources that still appear to be attempting to adhere to the Caighdeán but still differing in treatment of the article, and also a strange assertion even in the official Caighdeán document that "de réir inscne an ainmfhocail, úsáidtear an nó na sa tuiseal ginideach roimh an mbunuimhir aon nuair nach mbíonn déag ag gabháil leis
", but then going on to say "ag oscailt na haon fhuinneog déag"
Out of curiosity, what were some of the variations reported by native speakers? To be honest, I'm often wary of these for some reasons, which sounds like a funny thing to say, considering they should
be the most reliable but the issue with Irish is a bit more complex, partially because of what constitutes a native speaker. That is to say, I've seen people identify themselves as native speakers because they come from a Gaeltacht but their actual mastery of the language isn't always perfect. Also, as a native English speaker, I run into native English speakers all the time who don't know the "correct" way of saying things. The same is true of other languages and as a foreign learner I strive to learn the most "correct" version of things that I can, obviously taking into consideration what people who speak the language every day actually say. It's an imperfect analogy, obviously, but I wouldn't expect a foreign German learning English as a second language to learn things like "ain't" as standard. That said, I'm always curious to know what natives say and do attempt to mirror that. It's a tricky subject though, for sure, and it highlights some of the less-discussed complexities of learning to speak a living language.