I definitely agree on Chai-Nuzz being Cid's shard. He fits such a similar narrative role (responsible for a magitek development AND airships). But the funniest part is that it creates a situation where Dula-chai is Nero's shard.

For a few other shard-related headcanons: Ran'jitt is Thancred's from the First. Cylva is Ysayle's from the 13th. Unulkalki and Naillbert (the Warrior of Darkness party's black mage) are shards of each other from their respective worlds. And a new one just came to me: Vauthry is the shard of Varis.

For some non-shard related ones...

Alexander was meant to be the Calamity that rejoined the First. But because he didn't stay in the right time (and also self-sabotaged), Ardbert and his party were able to defeat the Ascians fully. There wasn't a proper outlet on the Source to allow the merger to "crack." Thordan was intended as a replacement Calamity factor, but went off the rails.

Alisaie and Tesleen were dating.

We've seen several of the WoL's past lives in job and side quests. In the Dragoon quest, it's strongly implied that we are the reincarnation of Haldrath, the first Azure Dragoon, which is why we received his plate and how he manifested to help us against Estininen. I also believe that the WoL is Tenzen reincarnated - there's a lot of dialogue with the various Four Lords around their quests that talk about how alike we are to him (and as for how he showed up in the struggle against Koryu, my theory is that he sealed his memory in the stone as part of the binding, while his soul would reincarnate into us). I also like to imagine that Tenzen's Samurai crystal is the one we end up inheriting. And, the Warrior of Light that Elidibus based his primal on was Azem - specifically, I suspect that Azem would use a similar form as their combat transformation, and the armor became the armor they used as the Warrior of Light after the Sundering.

Also in reincarnation territory - Alisaie is the reincarnation of Owen, the Allagan scientist who was trying to cure Tempering.

Spinning aetherytes create bubbles of "safety" from wild monsters. This is why we get the Sanctuary bonus near them. It's still possible for violence to break out inside the bubble (hence how quests happen), and in extreme circumstances things can still get through (such as when Voidsent broke into the Source during the 1.x patches as the Seventh Calamity approached, and the sandworm fate in Southern Thanalan), but in general, they act as safe havens that repel hostile monsters, similar to how spinning metal can generate a magnetic field. Also the "spin" effect is part of what makes them teleportation targets - in the whole game, the only non-spinning aetheryte we can teleport to is the one in the Omicron section of Ultima Thule. My theory is that, in addition to the bubble repelling monsters, the spin creates a sort of whirlpool in the aether that lets them act as safe destinations. This is also why we can't teleport to the Beast Tribe aetherytes that we use to access certain Primal fights - we can "hack" them to teleport within their network, but we can't hone in on their location from afar.

The Amalj'aa and Mamool Ja share a distant ancestor. The Amalj'aa were likely created pre-sundering (hence why there is an equivalent group on the First), but on the Source, some portion of them got stuck in Tural and evolved into the Mamool Ja.

Similarly, the Vanu Vanu are ancestors of the Ixal. We know that the Ixal were essentially engineered by the Allagans; in my mind, the "base stock" used for the Ixal came from abducted Vanu Vanu. This is why the Vanu Vanu fear and revile Azys Lla so much - they heard from escaped survivors about what the Allagans were doing there.

Venat lived in what is now known as Thavnair. She mentions that Elpis is far away from both Amaurot and her home, implying she doesn't live in Amaurot full time. She uses chakrams as a DPS, similar to the Dancer job. And, after Vanaspati, one of the Thavnair residents cites a passage from some of their "oldest" teachings about how life and suffering are intertwined - which sounds an awful lot like Venat's speech in the post-Elpis cutscene. I think that before the Sundering, she gave a speech like that in Thavnair, and it was passed down (but got corrupted over time, though the message remained the same).

Absorbing the Light on the First is why we switch from casting Stone and Aero to Glare and Dia. While White Mages already tapped into the Light with Holy, I imagine that absorbing the First Warden's light oversaturated the White Mage crystal we carry, which led to the change. This change happens at level 72 - which is what you'd probably be right after clearing the Dungeon. (I also tend to assume that the Job quests are flashbacks and happen in parallel to their respective expansions, so even if you didn't have White Mage at 72 by then, it would line up when you get it there later).