Although there's always the possibility, I would kind of prefer if we didn't start with a Dive to the Heart in KHIII.
The OP's suggestion for how it would work is really great, but I would almost prefer it if we did that intermittently throughout the course of the game. Like how in KH1 Sora has to lock the keyholes, in KH2 he's opening up the pathways, maybe in KH3 his goal could be to unlock the hidden portions of his heart and those he holds within it? On the other hand, it sort of feels like that was the point of his journey in DDD, but I never deciphered what was actually accomplished versus what was just introduced conceptually in that game.
I also think the final battle should involve a dive into Xehanort's heart. It would make sense if that was the only way to really defeat him at this point. Go right to the source.
I still want my Kairi in SoS tutorial and I will fight for it.