Tiber Septim=Hjalti+Wulfharth.
+Arctus. Although we've already run into problems because in the Heresy, Arctus is pretty pointless.
Through Hjalti he was a Dragonborn, got Aka's blessing;
And here you're mixing Heresy and Orthodoxy (which is good), because Hjalti of the heresy is just a trickster, while Talos of the Orthodoxy climbs the 7000 steps (a story too good to pass up). The whole Dragonborn things seems to enshrine it anyhow.
through Wulfharth he was thought to be mantling Shor, because Wulfharth was mantling Shor, a ruler in exile.
Hmmn... Let's return to the main point. The
betrayal, however exactly it is acted out, is what seals the Mantling deal. The betrayal in pursuit of Numidium. Wulfharth wasn't mantling Shor, he was an incarnation of him. And the betrayal isn't Shor-specific; it fits all myths.
As "Tiber Septim" was formed, even Wulfharth had left him, a Tiber Septim was still his own person, and would not be split back to Hjalti.
Not sure what this means.
For the Dragonborn part TIber Septim conqured the White-Gold Tower, whose seat was then for a dragon-blood-bearer.
He gets the Amulet of Kings from Sancre Tor, following Reman's path to the Covenant in a more PG-rated way. And the Dragonfires, to make it official, sure.
And he in turn conqured all man lands. If Tiber Septim was only a Dragonborn, like Alessia or Reman before him, he would have to stop here.
I think it runs off the rails here. Without getting into the issue of his mythic status determining his military success, we have Reman on record as conquering the entire known world. What this means is very vague, but it clearly extends beyond Skyrim, Cyrodiil and High Rock. The 1st PGE hints of Summerset's humiliation at Reman's hands, but I choose to interpret this as some Concordat-like enforced peace settlement short of annexation.
But as Tiber Septim did shared a Wulfharth part, he went to conqure Morrowind, and though not in a absolute millitary mean he did succeed.
Actually, Reman came close to conquering Morrowind by main force. Only his assassination stopped him short. Tiber conquered because of what Vivec say in him. And he only conquered Summerset because of Vivec's treaty gift on Numidium. (Although the legion probably outmatched Vvardenfell's forces.)
The Tribunal lose due to lack of power from Lorkhan's Heart. The 'Lorkhan-Power' was then striped away from them, so they could not resist another Lorkhan-Power bearer without much sacrifice of their own people, as they had done before.
This seems to be a bit of an inventive stretch on your part. The only talk about power levels we hear about is Dagoth preventing the Tribunal from bathing in the energies of the Heart. That is a very different kind of divinity, and as you have pointed out, Wulfharth is a creature of Shor. Lorkhan is notoriously fractured and capable of existing in multiple contradictory forms simultaneously. Look no farther than the Songs of King Wulfharth and the battle there.
Then Tiber Septim gained Numidium. He used Wulfharth and Zurin Arctus to activiate it, then with Numidium he conqured Summerset Isle. It was Talos who conqured Summerset Isle, because the conqurer was Tiber Septim+ Wulfharth+ Zurin Arctus, the latter two mixed up an Underking, with Zurin Arctus merged into its body and Wulfharth its heart.
And conquest is important, but somewhat holistically and ambiguously. It's that encounter in White Gold that really matters. Betrayal and dismemberment is the name of the game. That's the Enantiomorph.