If we're bringing everything to bear, something that struck me:

The relic is mentioned as being from the Fifth, or possibly early Sixth, Astral Era. Namono mentions that he 'serpent' in question to be a metaphor for the Lifestream. But on top of all that, an interesting wrinkle is that it uses an Allagan tomestone of some kind, or at least something resembling it. That actually knocks us a little, because it's not until the Seventh Umbral Calamity that Allagan relics were being unearthed enough to be found en masse; the capital city was buried by the Fourth Umbral Calamity, and the Seventh forced a bunch of them open.

So, we've got a few bullet points on this to help us narrow it down there. Now, we have to be aware that the source of the relic and the source of the language aren't necessarily one and the same, but the former does have to come after the latter, and the former also has to be in a position to be aware of the latter (since the Golden Dhaya is, appropriately, a Babel Fish but is working from a predefined knowledge of languages).

I'm wondering if perhaps at least one part of this mystery is Gelmorran. We know they had some knowledge of death and the Lifestream (although it's not clear how much since modern necromancers keep muddying the waters), and are exactly the type to use a serpent metaphor for it. On the other side, being a subterranean Eorzean civilization, they're also exactly the people I'd expect to have found Allagan tomestones before Dalamud unearthed them. And since they're both descended from an ancient civlization with significant international relations, albeit negative ones (Amdapor), they'd be the type with a fair amount of knowledge of at-the-time extinct languages. And they'd probably have vested interest in understanding some present ones, too, since they were living in hiding from the inscrutible Elementals.

I just want Gelmorra to matter, damnit!