Oceiros' Soul allows you to make Seath's weapon and sorcery because he literally wanted to become like Seath "Oceiros went mad trying to harness his royal blood for a greater purpose, leading him to the heretics of the Grand Archives, where he discovered the twisted worship of Seath the paledrake."
The message of being able to create his weapon and magic from Oceiros soul is pointing out that his transformation was successfull and the king reached an advanced state close to his ideal "Seath's research seemed to strike a chord with old Big Hat who, in his mad, disrobed state, made divine works such as this, his own. Oceiros was no doubt edified by this."
Aldritch Soul confirms it because its the same logic ... by giving Priscilla's signature weapon with his soul the text its implying something.
"Aldrich dreamt as he slowly devoured the God of the Darkmoon. In this dream, he perceived the form of a young, pale girl in hiding." Aldrich is dreaming about a pale girl in hiding ... and with this thoughts you can create Priscilla's weapon ... do you think they made this randomly or again to imply something the same way Oceiros's soul does? It seems like we agree that there's a least a connection between Gwyndolin and Priscilla the means doesnt matter.
Now we can indeed be sure of their relationship ... Gwyndolin and Yorshka both have draconic traits but the thing is their brothers ... "A sacred chime belonging to Yorshka. Her brother, the former knight captain, presented her with this medium together with another gift: her name." But she can't be a daughter of Gwyn because Filianore is the last one "For the pygmies, who took the dark soul, the Great Lord gifted the Ringed City, an isolated place at world's end, and his beloved youngest daughter, promising her that he would come for her when the day came."
This means Yorshka and Gwyndolin share the same mother and both inherited draconic traits from her (since i don't remember Gwyn having those)
"I'm not saying it's weird that he opposes the Darkwraiths. I'm saying it's weird that he does that and then seemingly doesn't interact with the abundance of humanity they harbor, if we assume that he, and his magic, does in fact have this inherent connection to the Dark." How could the last god left in Anor Londo and last son of Gwyn ever think of interacting with the Darkness in a way different than crushing it as you provided plenty of examples.
Gwyndolin being a male was in fact kept a secret because otherwise Lloyd would not have taken the Throne and title of King of the gods if they knew there was another son of Gwyn "A divine ring granted to the Darkmoon Gwyndolin in his youth. Causes males to perform female actions, and vice-versa. Gwyndolin was raised like a daughter" "The power of the moon was strong in Gwyndolin, and thus he was raised as a daughter" Gwyndolin was dressed as a girl since birth and raised to behave like a girl ... everything else you said about Gwyn is right
The Nameless King is Gwyn's Firstborn
"A dragon hunting weapon from the age of the gods. The earliest form of the cross spear, serving as both sword and spear.
Its owner was the Nameless King and deific hunter of dragons. The swordspear is imbued with lightning, of which he was the heir."
He hunted dragons before the Age of Fire and he was a god that inherited "lightning" .... but if this wasn't enough "The Nameless King was once a dragon-slaying god of war," he was also a War god that took part in the war against the dragons ... but if this wasnt enough "This golden crown, buried amidst long strands of bristling ash, is said to closely resemble that of the First Lord." he wears the same crown of Gwyn meaning that he inherited the throne
"Once a slayer of dragons, the former king and wargod tamed a dragon" he was both a king (of what if not Anor Londo?) and a God of War and a slayer of dragons ... this is the most direct confirmations you'll ever see in Dark Souls this is overwhelming logic.
He was a God of War of Anor Londo that took part in the War against the Dragons and inherited the lightning, wears Gwyn armor and became a king but now is "nameless" (these are all facts taken from the descriptions above)
In the end sadly this wiki invites entire sections of lore that are written without sources and are incomplete, confused and incoherent or with terms like "It's implied and its possible" ... examples are even the most searched pages like: Furtive Pygmy, Oceiros, First Flame, Gwyn etc ... entire paragraphs have things like "Although not explicitly stated, it is implied" so its logical that someone coming here for the first time would think that indeed speculations is accepted into ==Lore==
Sorry for my english, hope everything i write is understandable