Yup, all the links are right. 虚構推理 Here is the Amazon series link for 虚構推理 (I guess they realized they could sell more by putting anime girls on the cover).
I knew about the other book clubs. In fact, I was kinda hopeful that if we did pick up one of those series we could skip past the volumes that have already been book clubbed, since I’ve already read them too 
But that’s a detail that’s unimportant in the scheme of things.
For pitching series, I was trying to choose series that had at least 5 entries and were more ‘high concept’ than just “all the books an author wrote with their recurring detective” (although I’m not sure Writer Alice and Nikaido really meet that bar either), so I don’t think there’s anything inherently wrong with 内田康夫, but if we are considering those kinds of “series” as well, we get opened up to a loooooooooot more authors (like Shimada Soji, Noritzuki Rintaro, and Ashibe Taku)
I have no issue with shorter books (and if the books are shorter maybe the club could fire more often?), but giving up both improbable architecture and locked rooms is a big ask 
One other series I meant to pitch is Kitayama’s Castle series Amazon.co.jp: 『クロック城』殺人事件 (講談社文庫) eBook : 北山猛邦: Kindle Store but I think it has both architecture and locked rooms, so maybe not