I love a good conspiracy theory, but man, attempted debunking can take the wind out of them sails for a good few hours! Still, I will address every theory with the same care I hold my own nutbag ideas to, so off we go!
EDIT: So, I accidentally spilled the whole theory out and wrote a novel. Oh, well. We'll get to my Loremonger articles and point-by-point analyses later.
Remember: Look for contradictions and inconsistencies in everything I say, just in case
I'm going to hop around for a bit clearing up a few misconceptions before I get started.

Originally Posted by
Mjollnir
This is the only sighting of the Sea Serpent since times of legend
The Sea Serpent makes at least three confirmed appearances:
- Shapeless Melody's leap over the echo ship
- The battle between the Knights of the Barracuda and the Serpent Reaver ships commanded by (Ascian-in-Disguise) Travanchet where it tidal waves everything in the vicinity
- A battle where local pirate gangs, including those aboard the Astalicia, drove the serpent back to the depths. Sthalmann implies to Reyner that it was the returning of the Rhotano Bloodcant tablet to the deep that actually caused it to leave, but this may have been a ruse to divert attention away from the horn (aka The Key; The Treasure) and steal the tablet for himself.

Originally Posted by
Mjollnir
On the Astalicia
It's never stated in a single instance that Hyllfyr is, all of the above, captain of the Astalicia, which serves as the base of the Marauders Guild, headed by the Bloody Executioners, which he is also the leader of, and he's a legendary pirate with unmatched reputation. All of these things are said separately in various places across various times in various story arcs. I think Anwyll was generalizing (though, you never know with him. Dude's the wiki-editing definition of a loose cannon)*, but the quotes are:

Originally Posted by
Baderon
Well, if ye be 'ells-bent on knowin' what 'appened th' last time that grisly beast reared 'is accursed 'ead, I suggest ye speak t' some o' the pirates what 'elped drive 'im back. <...> Ye seen the towerin' dromond down at th' docks? That there be the Astalicia―'ome to the fiercest buggers in Limsa. Was a time when them marauders 'd cut yer 'ead off fer so much as lookin' at their shadow. Cooled down a bit now their cap'n be retired. Opened up their ship t' the other pirate gangs an' started a proper guild o' their own.
Legends Adrift

Originally Posted by
Gunicum
Lest you doubt the extent of their degeneracy, no less an authority on acceptable standards of villainy than one
Captain Hyllfyr has refused them a voice on the Astalicia.
Ceruleum Shock

Originally Posted by
Mynadaeg
To make matters worse, Limsa's pirates have already begun to rouse their crews for a fight, on the back of rumors that the Bloody Executioners are planning to pull Merlwyb from her perch and promote their captain, Hyllfyr, to Admiral.
Shot Through the Heart

Originally Posted by
Merlwyb Bloefhiswyn
As you can see, I have summoned others to this meeting─Commodore Reyner of the Knights of the Barracuda, Grand Storm Marshal Eynzahr Slafyrsyn... and finally, Hyllfyr, Captain of the Bloody Executioners, and voice of Limsa Lominsa's pirates.
Deus Ex Machina

Originally Posted by
Mjollnir
"One-Eyed" ...
It took me a while to realize this, myself, but I'm about 85% sure that Sthalmann is not referring to Hob's ship or the events of Shapeless Melody at all when he talks to H'naanza.
In fact, if you look at your two quotes back-to-back, it should make it even more clear that, most likely, he is referring to the Astalicia. In 1572, the fact that the Astalicia is a pirate ship (everything I said up thar ^) is Lominsa's "worst-kept secret." but it was still a secret back in 1562, considering Hyllfyr hadn't settled down and opened it as a guild yet.
Thus, I think it's far more likely that Hyllfyr is legit. That the quotes above substantiate my previous claims by my own standards at least, so I think it's safe to say he was well-known in '62. Also, the theory about a Faux-Hyllfyr is based on Sthalmann having one eye and Hyllfyr having two, but also demands that 10 years is all it takes for people to forget the face of a pirate everyone knows, respects and fears despite the fact that he looks just like the guy who killed the Admiral in a failed coup.
Before I move into the scenario I think is more likely at this moment, I'll, of course, have to address your question: Why would a two-eyed pirate take a one-eyed nickname? To make him more intimidating. One of Lominsa's greatest pirate stories is that of One-eyed Wylfred (a story told by Erik).
My current theory, that Shapeless Melody takes place three months prior and Sthalmann becomes Commodore due to a Tident afterwards, does fit this timeline and takes this into account, even if it can't identify the echo ship or why Sthalmann was there. My thinking is that, as a pirate, Sthalmann would have been aware of the Astalicia regardless of whether he was on that ship's crew or not. Follow this line of logic.
THIS IS ALL FACT-BACKED, BUT STILL PURE SPECULATION:
Whatever ship he's on, he at least knows enough of the serpent's legend to realize that it's in the water and scream, "Brace yourselves!" before it reveals itself, much to his shock.
- Why does Sthalmann know the serpent is coming by the movements in the water?
He knows the legend. But if the serpent is real, then Swallowtail Roam must be real! The treasure must be real! If he could claim it, he could rule the seas!
- But, how could he possibly get the treasure?
Once the Knights of the Barracuda know Swallowtail Roam has risen, they'll lock the site right down. He'll somehow have to garner enough power with the Knights, before they find out about Swallowtail Roam, and lock it down for himself. He wants this kept as quiet as possible; that's why we hear it have two names, that's why he gets angry when people mention the sea serpent, this is why he manipulates knowledge about what it's after.
- Where do you get that kind of power over the 'Cudas?
There's only one way: your captain wins the Trident. He's already respected among his crew. Hell, they're probably already going to enter. They just need to win. Somehow, legitimately or not, Sthalmann helps them win.
- "Alright, I'm Commodore, now what?"
Rumors of the sea serpent are spreading, as are those that a strange island has appeared. He can't just tell them Swallowtail Roam has risen, so he denies the serpent and forms a special unit to investigate this "Seal Rock."
- "Alright, this is going pretty good. Hey, wait..."
Before the Seal Rock Unit can be formed, a civilian trade ship from another land is registered with the Lominsan government. But isn't that... IT IS. It's the Astalicia. "Oh, Hells no."
Sthalmann knows what the ship really is, so he immediately locks up the entire crew. No matter what happens, he cannot let a rival pirate with that much power and respect gain a foothold in his very city within his very government, but what can he do about it? Hyllfyr is private now, he doesn't let himself be seen; there's just no proof!
Sthalmann thus must stay in town and deal with this, and he can feel the treasure slipping from his grasp.
Think of all of this in context of the H'naanza quote you mentioned earlier. He tells her that, despite the lack of proof, this ship is without a doubt a pirate ship and he has to deal with it. H'naanza herself muses that this pirate conspiracy might be related to the sea serpent rumors. This is why Sthalmann flies into a rage - not only does he have to deal with this crap from Hyllfyr, but he can't even talk to anyone about it without them being like, "Well that must be related to that sea serpent you don't want anyone talking about!"
- How can he focus on Hyllfyr without losing the Treasure?
He needs a plan. First, he recruits Merodaulyn into the 'Cudas and places him on the Seal Rock unit. The Sanguine Sirens want a man in the 'Cudas, and Medodaulyn will leave them in an instant if he could be in with the next Admiral, instead. Then, he recruits Emerick from the Krakens Arms. He knows Emerick has dealings with the Sahagin's Serpent Reavers; his niece Sisipu saw him conspiring with them to attack Oschon's Torch.
While Sthalmann deals with issues in Limsa, Emerick schemes with the Serpent Reavers. He gives the 'Cuda charts to Travanchet and informs him that Merudaulyn will assist him in wiping out the Seal Rock Unit.
Emerick then backstabs the Sahagin and has his captain, Caravallian, sail right past the fight and raid Seal Rock. He hides Sthalmann's treasure away and none are the wiser.
Sthalmann then "arrests" Emerick for his role in the destruction of Sisipu's village and attacks on the 'Cuda fleet, then safely hides him away at the 'Cuda's sequester ship. Here, he can regroup with Emerick and Merodaulyn and execute the final part of his plan: kill the Admiral, activate the treasure, rule the seas.
- Unfortunately, Travanchet turns out to not be a Serpent Reaver at all.
This Elezen is able to blend into Lominsan crowds, but is in with the Sahagin, and deals with the pirates who have infiltrated the 'Cudas ... but he is loyal to none of the forces on which he spies. He's an Ascian.
Before Sthalmann can do anything, Tavanchet comes at him with all of his might. The sea serpent tries to come for those who took the treasure, but succeeds only in wrecking the fleets, severely wounding Emerick, and causing Merod to go MIA.
To make matters worse, Hyllfyr, though a pirate, is loyal to Lominsa's roots, safety, and values. The Astalicia sheds its subterfuge and leads the charge against the sea serpent, thus securing even more respect and causing the Lominsan government to look the other way on their docked "trade ship" so long as they open a "proper guild." This may be another reason Sthalmann says that the Rhotano Bloodcant tablet returned the Serpent to the depths. He wanted some credit.
Travanchet returns and is able to take the treasure from him and disappear, leaving Sthalmann with an Admiral dead at his hands and no way to take power. He falls into disgrace and Emerick takes on a new identity and leaves for Ul'dah.
Honestly, I didn't meant to spill the whole theory so soon.
The only thing stopping me from getting up on a mountain and yelling, "I've done it! I've finally done it!" is that it completely ignores Y'sholta's role. This is why I've started with those two simple questions of Shapeless Melody. If Sthalmann's role, or the ship's identity, contradict this at all, a lot of it is in danger of crumbling. If it all holds up, however, we end up back at Y'shtola.
We have since seen her in full Archon mode, which, to me, says that maybe she's using Circle of Knowing methods to investigate through time, trying to pinpoint the exact moment that the Ascians took the key out of play into their own dimension and prevent it from happening. This is why she gets closer and closer to the right point in time, it's how she teleports into places she has no right to be and out of imminent danger, and then shows up ten years later to get involved in Dalamud, and then 5 years later still for whatever happens in ARR - and doesn't look a day older.
If this is true of Y'shtola, then she's just doing her Circle of Knowing + Archon deal when in comes some newbie echo-hopper who crashes the party. She loses the key and goes back to the Circle of Knowing. When the Seventh Umbral Era begins, there's the echo person again; better team up.
If this is not true, then her actions are much more concrete and will likely dramatically interfere with my Sthalmann theory, as she'll be much more involved; though I must say, if this is the case, she ages ridiculously well. Like, lalafell well.
But there you have it. What do you think? I wish I could just lock this up! *n*
*SPOILER:
Anwyll is Anonymoose