Ability scores shouldn't really affect your ability to be any particular alignment. A high wisdom character who is chaotic could still be reckless or disrespect legitimate authority, because all his high wisdom means is that he has a wealth of real world experience and greater philosophical justification for behaving in that manner. People who disrespect authority aren't necessarily fools, and there are plenty of characters in fiction and people in the real world who are both described as wise and in constant conflict with orderly society.
"Whatever works" is going to be neutral. Just as a Lawful character might occasionally default to taking an ordered approach, a Chaotic character is going to occasionally default to a chaotic approach, even when something more measured might be more successful. In fact, it's literally in the alignment definitions that Neutral characters follow rules when they want, and break them when they want. The idea that "lawful slavishly follows the rules even when its stupid" and "chaotic doesn't do that" isn't supported by any version of the alignment system. Alignment on L v C is about your biases.
I agree, organized crime can definitely be Lawful. I don't know much if anything about the history of the Yakuza, but I do know that in other "organized" crime syndicates, the laws and oaths were really just tiny barriers for the foot soldiers to not behave in ways the upper crust disliked, and were frequently broken when they became inconvenient for folks at the top. So how "Lawful" your organized crime is will depend on whether or not folks follow those Laws even when they become an inconvenience. And of course, both Lawful and Chaotic characters can exist in an organization that's setup as Lawful.