So it turns out that the Allagan Eureka we saw in the 6.3 live letter isn't from nowhere! A fair few people knew this already, and it's actually explained by an NPC in-game. But since nobody had copied down this NPC's dialog out-of-game as far as I could find, I've decided to get it myself.

All of this is from the Expedition Scholar in Eureka. The Scholar's actually hanging around the home base of every Eureka zone, but mostly only talks about the aetheric wackiness of the island, or to sell you Aetheric Stabilizers in Hydatos. But in Pyros (the third zone) she's actually available to talk to you about the original Eureka, the one that our Eureka was named after. I've copied it all down here:

Quote Originally Posted by The ancient legend of Eureka
The first thing you need to know about the ancient legend is that there is more than one! Though, I suppose you could say that the various extant fragments add up to a single legend's worth of information.

Alas, given the myriad sources from which it's been compiled, what we know is full of contradictions. But what we can say for certain is that it was a grand labyrinth constructed in the twilight days of the Allagan Empire, in which weapons of terrible power were squirreled away!

I say we can say this for certain, but due to all the contradictions surrounding other details, most scholars have long since dismissed Eureka as a faerie tale deserving of no further scrutiny.

At least that was the case until the Seventh Umbral Calamity unearthed the Crystal Tower, which was also previously believed to be wholly fictional. After that, well, everybody stood up and took notice, including the Sons of Saint Coinach and the Students of Baldesion.
Quote Originally Posted by The location of Eureka
I'm glad you asked! You see, according to most sources, Eureka was buried beneath the Crystal Tower!

The tales sometimes describe the structures as being related to one another in some fashion, so when the Sons of Saint Coinach started poking around the Crystal Tower, there was an expectation that they'd find evidence of the legendary labyrinth as well.

Unfortunately, their efforts thus far have yielded nothing save an increasing certainty that wherever Eureka is, it is definitely not beneath the Crystal Tower. But hey, knowing where not to look is still a step in the right direction, is it not?
Quote Originally Posted by The treasures of Eureka
That there is the million gil question, isn't it? What wondrous and terrifying weapons of unimaginable destructive power could be contained within Eureka?

Untested Allagan prototypes with the potential to reshape the world. Cursed relics obtained by Archmagus Noah through a pact made with the rulers of the voidsent. Or perhaps sacred treasures bequeathed to mankind by the golds of eld! The possibilities are endless!

Alas, this is one of the points of contention upon which the extant sources do not agree. It may well be that the authors of these accounts from the Third Astral Era had no idea what weapons had been hidden inside Eureka, and so let their imaginations and their writing run wild!
I love that this actually has nods to both the FFIII Eureka, and the original plan for FFXIV's Eureka. For those not in the know, in the original FFIII Eureka was a hidden bonus dungeon, which contained both a bunch of bosses and the game's strongest jobs, Sage and Ninja. If you want to check it out now, it is in the pixel remaster, but isn't in the 3D version.

We've learned over time that there was a plan for a Eureka similar to that original in FFXIV; it was apparently what Nero's wrist communicator/detector thing blipping at the end of the Crystal Tower was originally supposed to be a hook for. We don't know what sort of content this original Eureka would've been, just that it was going to be located under the Crystal Tower.

And, for what it's worth: the name 'Orthos' was one of the alternative spellings of what's now commonly called Orthros, a two-headed dog from Greek and Roman myth; child of Echidna and Typhon and brother of Cerberus, it was killed as part of the Labors of Hercules. Orthros has never faithfully appeared in Final Fantasy, but the name was likely-mistakenly given to Ultros in a few early translations. Not sure how much any of that could matter--FFXIV very rarely does faithful mythical adaptations--but I do notice that with the exception of Hercules, every character I mentioned in this paragraph appears in FFXIV as a voidsent. A pattern of importance? Who knows, at this point.