#additional thoughts:

The shuffles all get roped into restoration projects on Earth between the 13th and 14th gundam fights, partially to have something to do alongside their training, partially out of inspiration by the common points of the Kasshus' and Master Asia's goals, and partially because netting their countries some decent publicity is likely to earn them favors during the Gundam Fight's off-years.

Sai is contacted by Kyral about an effort to clear out the infamous buildup of trash and cadavers on Everest; he wants Sai to leverage Neo China's help as something of a reparation kind of deal and Sai goes sure why not.

Sai recruits Argo because Bolt Gundam is built to withstand the cold, and he thinks Argo and Nastasha could help reverse engineer that quality to enable the use of their Gundams as both heavy work equipment and protection from the harsh environmental conditions that normally prevent this kind of operation.

George gets involved because someone he knows has a distant relative who died on the mountain a century ago, and they wanted him to check in with the forensics team on the project. This detail is important because eventually it becomes clear that there is a mystery to solve (that I myself haven't figured out all the details of yet but broadly know the setup and conclusion); DG-infected people are disappearing and not being investigated due to stigma. Our heroes are naturally going to be pissed about this, and will need an "in" with the field if they want to do anything about it.

First massively self-indulgent element: The forensics/body identification team inexplicably includes the real-world author Kathy Reichs, who somehow exists in this universe, and there's a little side bit about her having written a Bones book right before the 12th fight that featured a cooked cadaver found inside a gundam after entry into the Earth's atmosphere. There are a lot of weird coincidences in the book that parallel the DG incident, which creeps everyone out, but the similarities are merely born of the writer threading the needle of being believable and interesting in a way that became very true to life.

What does become relevant is when the Shuffles eventually meet up, she's able to explain the implications of a bunch of weird shit the fighters discovered (also Marie Louise read her book, and one of the in-universe liberties Reichs took writing about the gundams' black boxes that she explains in the afterword leads to ML realizing something important; that Neo Germany does not have its gundam's remains.)

While the Everest project is happening, Domon, Chibodee, and Allenby all want to continue their training somewhere on Earth, and receive a proposal from (an OC of mine who is) a historic preservationist (and an acquaintance of Allenby's): she has acquired the grounds of an abandoned castle in Europe* after submitting a plan to restore it, and needs to hire people to help with the labor.

*the castle is probably somewhere in Germany because I also want this pitch to have drama over Schwarz (pre-13th fight), Schwarz (Kyoji), and Schwarz (the next guy who was supposed to inherit the mask when the older ninja retired). Also Germany is fucking pretty.

In exchange for the help of the three gundam fighters, they and Rain get paid, plus room and board anywhere on the grounds, plus full access to the grounds and miles of sparsely-inhabited countryside for training purposes, and the privacy and ability to practice with their gundams that comes with being in the middle of fucking nowhere. Rain sets herself up to work a clinic in the next town over as well as practicing pro re nata wilderness medicine (I'm convinced every medic supporting the gundam fight would need to be able to do this.)

The group involved in the Castle project sticks around for a time, makes some good progress, and engage in occasional Shenanigans that come up when you put a bunch of weirdos in a Situation.

They aren't in town a lot save for Rain, but when they are they eventually start to pick up on gossip and news about the Mysterious Disappearances correlated with DG cell infection (as well as details that turn out to be important later). Eventually Rain brings this to Domon and Chibodees' attention and they decide that, yeah, this is tied to the DG, this is their problem, they should convene with the rest of the Shuffle Alliance about it.

Also of course Schwarz is involved because I'm the one writing this; the culprits' DG-tissue harvesting operation relies on having him captured and helpless, using cells from his body to "update" other victims' DG infections to a less aggressive strain. One thing I haven't decided is whether I want a reinstantiated Wong to head this shit, or make up my own morally bankrupt opportunistic asshole looking to twist the DG to their own benefits. I also need to decide where on the planet the center of all this insanity is, and it needs to be a place that isn't going to have any unfortunate implications (because that's a genuine risk with dark story elements)

... That's about as much as I have that is thought-out enough for me to explain. I return to thinking about this scenario a lot because it puts most of the characters way out of their element (and has a bunch of details that appeal to me specifically), and it kind of evolved into an incomplete plot outline that I don't currently have any plans to flesh out.