You'd still have rank within the 'main family', though.
Try not to focus on being a 'gang member'; focus on being a Yakuza member. That sort of focus will give the character more scope, put him into a better framework, both mental and 'real', than being part of a quasi-seperate 'crew'. He may actually be a 'crew member' - and considering the age range, unless you're playing a 50-something shadowrunner, I strongly recommend him being 'only' a member of the original crew. Becoming Shategashira/Kyodai would have taken time - at least five to ten years - which you really aren't going to have, considering the mob war was in '58, and if you're playing at current time - which is now '75 - it's almost 20 years later.
What I'd really like to point out, though, is that your background makes a complete break with the Yakuza. There's no need to take either Sworn Soldier or Made Man; you're no longer either. You left Shotozumi because he wasn't loyal to Watada; you left Watada because they saw you as, well, a loyal dog, and you were tired of it so you left. At this point, you're a late-30's to early-50's (if you ran your own 'gang') has-been never-was, basically broke and unemployed. You're not on your way up, you're on your way down, and for all intents and purposes you've got one foot out the door and the other one in the grave.
Were I using the character (who's going to be at least 37-38), while I would have him make essentially a break with Shotozumi, being 'an American' in Japan may not be the total disad you're thinking. If you're a human Japanese Yakuza coming from a human Japanese Yakuza family, then moving back to the homeland to support the main rengo is going to put you in the sort of camp that a fair several others are going to be in. Maybe you do work your way up to running your own crew, and yes, it may become clear that you're never going to get any higher, but ...
... are you going to be playing a mook, or are you going to be playing an assassin?? A mook is gonna be breaking fragiles, like windows and legs. He's going to get his orders from a shategashira, or maybe from a wakagashira-hosa. Do you really want that for your character? Or do you want the semi-outsider who the wakagashira, and maybe the oyabun himself, speaks to on an irregular but semi-frequent basis, saying, "I'd like you to take care of the problem that is respresented by this person," and then you go out and whack the guy.
The former is your on-your-way-down guy who's resentful about being treated like a loyal pet for the last two decades, who's trying for one last stab at glory in his old stomping grounds - a guy whose ties have frayed so much they no longer bind. The latter is a still-on-his-way-up or still-on-top guy, who remains loyal because even though he isn't going to become a wakagashira-hosa, he already kind of is, because he's a specialist with a special set of skills. He's a go-to guy, and though he may be in minor disgrace right now, it's minor and it's not going to last, he's just over here in Candletown cooling his heels until his boss is no longer quite so hot under the collar.
Both have lots of opportunity for RP. The has-been never-was former character has a lot of regret and desperation pre-loaded into him - sorry, perhaps, that he left advancement opportunities with Shotozumi for a dead-end job in Japan, desperate enough to go perhaps a little further than he really can any more, writing checks that his body can no longer cash. The local Yaks don't like him, he has no safety net, and nowhere left to go but either down into obscurity or out in a blaze of glory. This is a 'flashy gangster' sort - loud shirts, big swagger, ready with a gun or a comeback. High injury rate, maybe, leading him to more and more desperate measures until he does something incredibly dangerous and incredibly brave and goes down in a John Woo film-ending thousand-bullet moment. Lots of fun, but let's face it, the style of the character is a relatively short-term thing, where he's going to succeed brilliantly or die trying.
The exiled hit-man, on the other hand, is a cooler customer - one with whom the local Yaks can operate, maybe with some remaining tension because he left, but relatively courteously for all that. This is the 'businessman' sort, with the correct bows and the quiet-but-dangerous smile, who is just on a 'working vacation' until he can get back to his real business. He's willing to take risks, sure, but he's more confident that he can execute them, he's more likely to plan ahead, he's going to calculate and make sure things are stacked in his favor. His reputation is working for him this time (hit man, remember) instead of against him, and while he's going to carry the groceries for his little old Japanese neighbor lady up eight flights of tenament stairs, if you insult him he'll whack your boss, your sister, her husband and kids, HER boss, and then your cat before finally getting around to blowing up your car, your house, and then chopping off your hands and feet - and, when your replacements have just healed up, showing up to cut them off again before finally killing you. He's a long-term character, basically.
So it's up to your campaign, your playing style, and what you want for the character. I prefer the latter, but for a shorter campaign, I'd certainly be willing to play the former ...