I think the Alduin seen in Skyrim is a dragon who has mantled Alduin, out of the subconcious need for the Nordic Aspect to devour the world and bring about the next Kalpa. The Aedra need to take an avatar to manifest on Mundus and that is what Alduin is, an avatar. He has not fully mantled yet and is so not fully divine, but is still partly a mundane dragon which is why he is able to be thrown forward in time by the Elder Scroll. It wouldn't make sense for something that is fully time itself to be thrown forward in itself. Alduin needs to feed upon the souls in Sovngarde to further his divinity by further walking the way of Alduin.
Alduin claims to be the firstborn of Akatosh, the first fragmented part that became a regular dragon, because he fully believes that he is Alduin, because he is. He was not so much of a mundane dragon that he could be defeated on Mundus, but neither was he so divine that he couldn't be defeated in Sovngarde where his soul is drained back into Aetherius.
As he was thrown forward in time and the Kalpa extended, his mirror-brother who seeked to extend the Kalpa forever spited him further by breaking him back into time just as the last fragment of Akatosh was born into a mortal body to create the last Dragonborn who was to crush the half-divine Alduin from the mortal plane and destroy the cycle.
Does what I'm saying actually make any sense, or have I just grossly mis-interpreted lore here?