So I have a couple of thoughts on a starting point:
Schism Never Happened - either it just doesn't happen or the disagreement between Cyclops and Wolverine that led to Logan haring off and founding the JGI simply didn't end the way it does in the book. The X-Men remain based out of Utopia and the game's plot threads pick up at that point. The continuity's a few years old, but this mode is niiiiiiiiice and simple.
Fallout from the Secret Empire - More controversial considering the Secret Empire event is a trash-fire and it'd require a lot more jury-rigging and figuring out what the fuck's going on considering how many books are ignoring or downplaying it, but basically the premise is that Hydra squatted and took a big old dump right in the heart of the Federal Government. While there are various groups trying to fix the damage such as the Avengers, the game focuses on "Nation X" - New Tian, which incorporates a lot of the West Coast, including California, and is goverened by the X-Men out of Utopia. Basically this cutoff point would be before the current X-Restructure that turned into X-Men: Blue, X-Men: Gold, etc.
My suggestion for why the X-Men would regather under one roof despite it all is basically: No one's sure if there's going to even BE a United States anymore after Hydra and FascistCap went at it with no lube, and someone found adult Cyclops alive.
In other words, more complicated and having to touch an event that's no hyperbole comic herpes, but with a more recent continuity point and the chance to try something new WITHOUT it being a Year One.
Despite giving the second more elaboration, I really like both.