What happens to the Alternate History? Without Stocke, the Ritual can't be completed there.
I just assumed that the AH collapsed into the Standard / True History. Stocke threaded between the two timelines enough that they might have just merged somehow. Or, you know, everyone in the AH eventually died after the desertification enveloped Vainqueur. But that would be sort of depressing, you know?
Open the White Chronicle before you fight the final boss. Notice how the timeline you're in is in the middle? It can be said that Stocke had indeed threaded the Standard and Alternate histories together, creating the True Timeline mentioned oh-so-long ago.
Red Oni isn't always indicative of personality; it can just as easily refer to behavior, especially compared to the likes of Eruca and Raul. Stocke's actions (jumping headfirst into danger, quicker to go with his gut, etc.) suffice to characterize him as the Red Oni in most comparisons, while his initially cold and withdrawn personality characterized him as a Stoic. It's actually quite possible for a Red Oni to also be The Stoic or for a Blue Oni to be Hot-Blooded (though the latter would be more difficult to successfully pull off).
That, and the relationship where he's the red half of the pair was under a different name, and with different memories. During the game's time period, when he seems to be much more withdrawn, he plays Blue to Rosch more often than not.