Heya, I'm getting back into this so let me know if you're still interested!

Since no one has run any full-game runs yet, this is unclear. My personal method had been, start timer when starting first mission, and yes quitting is allowed. But I haven't finished a full-game run. For my individual mission runs, I stop the timer the moment the goal is complete. (using in-game time, so the log screen for 'objective complete' or what not is the actual time, with real-time as a tiebreaker)

I kind of like the idea of a gimmick "real world" run, where you have to leave the mission "naturally".