Look into EngineMapsSettings class within the EngineSettings API module, the Engine code uses it to read what GameInstance class your game uses (that dropdown menu property in your Project Settings. I think though, you’d have to compile UE from source code so you are able to modify it as per your needs (i.e. choosing before the game starts, which GameInstance is appropriate for the detected platform rather than what is selected in that drop-down button.).
EDIT: I don’t remember last time I looked into it, but perhaps you could derive from it and write that custom logic yourself?