Nice catches! My notes just say "1522 and allusions to it," so I kinda glazed over the contradictions relatively unnoticed, lol.
The ARR bonus disc has a few typos due to the time crunch and the fact that you can't hotpatch a Bluray, so that'd be my first suspect for the broken piece.
In its time, Rise and Fall made the claim that Garlemald was a remote Republic up until roughly fifty years ago and that cleared the fact check. Short version, Solus, a popular and successful Legatus, helped transform the Republic's military (with the aid of the father of Darnus) using resurrected Allagan machina modified to run sans magick. The popularity from this (and his victories on the battlefield) catapulted him from Legatus to Supreme Commander (aka Dictator). He then conquered Ilsabard and transformed it into the Garlean Empire, which then moved on Othard.
The Gubal Library piece (naming conventions) is something that Koji has been trying to get out for a while, either here in the forums or in the game itself. It's likely that this piece wasn't written hastily and is thus accurate. Here, we see the title ZOS already exists for Emperor. I'd wager that 1522 was the official transformation of The Republic of Garlemald to the Garlean Empire.
Between 1522 and 1557, we know Galvus conquered the remaining Ilsabardian nations, as well as the eastern continent of Othard, but which fell how quickly is a little murky. 1552 may be a typo that mixes the important dates of 1557 and 1522 and not actually be important at all, so I wouldn't take it as a given (yet) that the narrative need fit that date in at all.
A big reason for my hesitation to fit the conquest of Othard to that date is that the Empire faced primal(-like?) entities in Othard and wanted to avoid doing so again so badly that they moved on Mor Dhona (Eorzea's aetherial epicenter) immediately after they had a foothold in the realm, then and refused to move on Eorzea for ten years after the assault failed and primals were summoned by our beast tribes. Either they didn't effortlessly steamroll across Othard in five years, or they lost everything they could afford to lose. To be sure, either way, it took a heavy toll on their resources, but I'm presently inclined to the former assumption because if 1552 was the start of the Othardian campaign and it cost them everything, how did they recoup to move on Ala Mhigo and officially start the Eorzean campaign so quickly?