Exactly, you said exactly what I was thinking. Other than Riku, Kairi is in the best possible place to find Sora. Actually, she might be the best course of action to take, because she's the one that has actually been to The Final World. As far as we know, Riku's never been. And logically, what did people expect she was gonna do? Thinking about it... If TAV is in the Realm of Darkness looking, RAX are going through their memories, and Riku and Mickey are doubling back through all the worlds Sora's been to, what exactly is Kairi going to do? She's not just taking a nap, she's searching for her own answers too. But unless she has a Keyblade in hand, nobody wants to see it.
Honestly when it comes to this series, I feel half of the criticism is legitimate... And the other half are people wanting the story to go THEIR way. And when it doesn't, that's when suddenly Nomura is a "trash" writer, Osaka Team is garbage, and the KH series is going down the toilet. If people hated it so much, you'd think they'd just give up the series by now and move on, since KH3 is a perfect place to do that, but a lot of it is just talk. They'll be back for the next game and KH4 and if not? Oh well.
I think your idea is on point, because the DDD vol. 2 game isn't going to need everyone else's story expanded. It'd basically be, "We ain't found shit!" and that's the end of that. The Fairy Godmother already told us that the key is in Riku's and two other people's dreams, so that's where the focus should be. Namine should be able to play a pretty big role here, so Twilight Town would get more focus, but other than that... I don't think there's a need for that much fleshing out.
Verum Rex is an interesting thing, because we don't exactly know why Yozora (a video game character in Sora's universe) is now real (or maybe has always been real) and has been given the task to save Sora. The angle I'd go with would be exploring Yozora's backstory, and what he meant by trials (I'm gonna go with the Reaper's Game because it just fits). Also explaining why for whatever reason, he's relevant to what's going on for the future, and why the Master of Masters is also in this world.
Also something to point out, that nobody has yet... When the Master of Masters does his heart symbol with his hands over the moon, if you look closely, you see the inside of the heart getting clear and focuses in. Which is pretty cool, possibly symbolic as well.
And I feel like the Master is playing everyone, because if he "dimmed, faded" from KHX's time and then wound up 75 years before KH3 takes place, clearly inciting a Young Xehanort, who knows if he's even really trapped there. Luxu says "He will return", but I think it's clear that not even Luxu really knows what the Master's overall goal is. Nobody seems to know. But I think he needs Yozora AND Sora, possibly.
Y'know, what if the "trump card" Luxord gave to Sora has Yozora on it? Or something related to him? He mentioned it "could turn the tables", and then we hear a driver in the Secret Ending that sounds exactly like him... Not to mention, Luxord also seeing through pretty much entirely through Xigbar's facade. Then there's Yozora's goal of "saving" Sora. So I'm thinking Luxord and Yozora might be on Sora's side. Or, there's a very important reason as to why they're helping him.
I wonder, maybe Kairi's managed to contact Yozora?