Did some offline thinking and wanted to elaborate on a point.
If you are logged in and playing, finish a game and your stats aren't counting, that means the communication between the console and their internal databases is being broken randomly.
Getting splashed post game to the main menu is becoming a default option. Goes back to my original post a week ago about what the issue is. Too many ways to get to game functions.
If you want to do a moment, there's two ways to get there. Simplifying the path to game modes would be an angle of resolving this.
The only way to diagnose would be recording gameplay for 4 hours, checking your stats every other game, or after a bounce out to the main DD page.