I am not going to be so foolish as to say that this character type occurs with anything like the frequency you find Caucasians learning superpowers from isolated Asian locations. Dozens of such characters were spawned in the early days of pulp and superhero fiction. Popular fiction as an industry is incredibly derivative. When someone sees a particular formula work, that formula ends up getting copied many times over. Most of these end up falling flat or else failing to be anything more than just a copy of the earlier stories. In the case of this particular trope, it has been done so often that it borders on being cliche.
For the other concept, the idea of the Asian woman raised amongst Western culture to pick up its skills and abilities, initially I sort of nodded and agreed: "yeah, that would be cool to see." Then, after a little bit, I remembered Larry Vincent.
Irene (or Eileen depending on translation) Vincent was born in Chicago to an Indian father and an English mother who loves guns and muscle cars. Her father was a gunsmith and Olympic-level marksman who ran a gunsmithing shop. Her mother objected to this, wanting Irene to be a violinist, and ended up getting killed by robbers when she came to serve Irene's father with divorce papers. Irene's father then ended up leaving to hunt down the robbers and Irene took over the store. She had her name legaly changed to her father's: Larry (due to the katakana for "Larry" and "Rally" being the same, she has been officially translated to be Rally Vincent despite the author stating this was an error) and has managed to convince the government she's 21 when she's actually 19 so she can sell guns legally. On the side, she does bounty hunter work and she is an amazing shot and driver (Deadshot/Bullseye level marksmanship with Johnny Blaze/Duke Brothers level driving). Beyond that, she has an encyclopedic knowledge of different guns and how they were made. The author is a gun-nerd and it really shows.
Rally fits most but not all the concepts of the "Inverse Iron Fist" scenario. She's a woman of Asian ethnicity raised in America who gains levels of skill that reach the point of being superpowers. However, she wasn't so much abandoned here and America is her native culture. She didn't have the sort of cultural isolation most of the powers from traveling in Asia set have.
A better example would be Kate Freelander from the television show Sanctum. As a child, her father moved the family from Mumbai to Chicago where he became a criminal. He was killed by a bomb due to gang politics, something Kate witnessed. At the time she was eight years old. Her mother then had her younger brother and they wandered about the States for a while before her mother returned to India. Kate has most of the same skills as Larry (though not nearly to the same level), being a general bad-ass with excellent skills using guns and driving cars, but definitely has that sense of isolation since she never lived in polite soceity the way Larry did. However, she didn't return to India until near the end of either the second or third season and that subplot was a bit overshadowed by the subplot of her Caucasian co-worker having a brush with Kali and sort of gaining temporary superpowers.
The main problem is that the trope won't be recognized as a trope because we are a heterogenous culture and while both Larry and Kate have extreme levels skill in firearms and driving, to the point of being superhero level, their genetic heritage is for the most part a non-issue. They act American, they have skills typical of American action movie stars and thus they are folded into the general trope of Girls with Guns or Action Girls. The formula of the Asian girl learning "Western" skills has been used but hasn't been repeated often enough to be labeled a trope.
Part of this is the fact female action heroes are still a much smaller group than male action heroes. The many various derivations of the action hero found in men are often repeated among their female counterparts, but the much smaller numbers of such characters means that these specific derivations rarely have the numbers necessary to be considered a type of character.
Another part of this is that the skills involved: gunslinging and driving; are not perceived to be exclusive. Not being in the hobby of shooting guns I can't speak to how much of a white exclusivity issue marksmanship has in reality, but the public perception is that anybody has access to learning to be a good shot. This robs the scenario of one of the key themes of the basic white-man-gets-Asian-superpowers scenario: the struggle to prove one's self in order to learn the secret techniques. These skills are also not strange and unheard of. The majority of the American public considers itself to have a strong understanding of firearms and gun battles (most of us are wrong about this, but perception is more important here).
That said, there is a struggle against exclusivity in the Inverse Iron Fist scenario, but it is a gender-bias rather than a culture-bias. Woman are very often not considered to be capable of being good at firearms. The women I know who are into gun collecting often speak of people undermining their expertise and skill in the hobby. By comparison, the basic Iron Fist scenario lacks the gender issue. In fact, the more common type of Asian warrior woman idea is noted as having had to work against the biased concepts of their own culture in order to earn their place. The issue of women having to work harder to achieve the same respect as their male counterparts overshadows the issue of trying to fit in to a foreign culture.
The scenario as stated also suffers from the fact that Asian countries practice gun skills. Even if there are almost no guns outside of the government, there are still expert marksmen and the public knows about guns and has something of the same level of perceived-understanding about guns that a lot of Americans have. They lack the exotic nature that allows them to stand out as something iconic. Granted, there are iconic gunslingers and iconic guns. The Peacemaker from Wynona Earp, the Colt from Supernatural, Dante's guns in Devil May Cry, the gun of Roland in the Dark Tower, Dirty Harry's magnum, Larry Vincent's CZ-75 1st edition, so on and so forth. But for the most part the public sees a gun as a gun.
The scenarios with the Caucasian travelling to the East and acquiring secret ancient skills would best see an inverse in the Asian coming to the West and doing likewise. You'd have to have something isolated and secret. So not just Texas, but some ghost town lost in the deserts of Utah or Colorado where a community of gunslingers have lived isolated from the modern American culture for well over 100 years. Even then, guns lack the ancient mystique that Asian martial arts have. To start off such a trope, you'd have to have something like the Chinese girl orphaned after surviving a plane crash get taken in by a community of lost Vikings in the Canadian wilderness and coming back with powers of rune magic and secret valkyrie fighting styles. Alternately, getting lost in some lonely corner of England and stumbling on an extradimensional stronghold of the Tuatha de Danan or King Arthur's court.
This runs into another problem. A lot of people in Western cultures see the ancient past of Asia as a sort of period of enlightenment and lost knowledge. Hence the plethora of books that make use of a shallow understanding or connection to Asian philosophies to sell their ideas. Meanwhile we see our own past as quaint and often backward. This is a sort of cultural bias of its own: we see ourselves to have risen above our ancestors while we see foreign cultures as having lost their greatness. If it turned out that King Arthur's Camelot continued on from an alternate reality and one of their own came into our current world, they would be more often shown as a backward fool learning about modern life than that they had some ancient secret of worthy note.
The biggest hurdle is the fact that women struggling to be accepted is sadly a nearly universal issue. In the real world they have issues getting equal pay and we've seen several instances where campaigns of harrassment have been directed at women. When a female character faces a struggle to gain respect and inclusion in a culture, the default focus of the story is on the fact that she is a woman struggling to be accepted. Looking at the Vikings in Canada scenario, it is conceivable to have such a culture where men and women are looked upon roughly equally, Vikings were remarkably more progressive about women than most of the cultures of the day, and have the focus be on her ethnicity instead of gender. However, once you get out into modern society, the focus of the woman acting in what is traditionally considered a male role returns.
This also won't end up recognized as a trope until there is a character for whom that scenario stands out as the strongest part of her story or character and then becomes incredibly popular. Popular enough to spawn multiple homages, expies, and outright copies.