@Ghetsis
Interesting writeup. The mystery of Fukurou's disappearing and reappearing Kakerou membership is one I couldn't figure out myself, so I kind of put it aside. There's definitely an oddity there where he apparently relinquished his membership before gambling with Hal, but also had one to give Suteguma. I had completely forgotten Lalo saying he had procured two Kakerou memberships (and also that he really liked video games) so it seems plausible that he just gave one to Fukurou to pass along to Suteguma, since Billy didn't want it.
I think you're definitely on the right track with Fukurou having some kind of god complex, considering how he talked to the Developers. He was outright thinking of just killing Hal instead of gambling with him, and probably would have if he didn't have Eba with him. The theory that he's following Lalo because he's special makes a lot of sense if we follow from that line of thinking, though Kakerou is just as special as Ideal. There's definitely more mysteries to unravel with this guy.
@Solano
I think it's possible that initially he was doing it for the thrill of it, to prove he was the best. I believe early on (Hangman?) Baku said he felt most alive and comfortable in a Kakerou gamble with his life on the line. It's not really a mindset most people can understand, but its one you see a lot in gambling manga like Akagi. RapidLord comparing it to Kyara/Yakou/etc wanting to stand at the pinnacle of strength is a good way to put it; puts it into a more understandable frame. However, I think somewhere along the line his priorities changed, probably when he befriended Hal. He changed his philosophy to gathering allies outside of the Kakerou structure so that they would be legitimately loyal to him and not just ally with him because he wins. We know from his conversation with Hal that he considers the most thrilling possible gambles to be when someone is left with nothing but only their life, and crawls all the way back for a rematch. Souichi took everything in the first StL except his life, and now I believe Baku is fighting for that ultimate thrill of facing Souichi (his friend Hal) in a gamble again, like The Prince Bee. This all goes back to the theory that Souichi can remember certain things that make a lasting imprint on him, like Eba telling him how to find him, or (perhaps) Baku saying that the pinnacle of gambling comes from someone making a comeback with nothing but their life.