Nan Zhong Quests are the quests in chapter 3 where you defeat Meng Huo. It's simply fastest because you have to walk the shortest distance to receive the quest.
And being fast to quit means you can have many tries to draw a card (each time you quit/complete a quest there's a small chance you draw a card).
I've completed all officer cards for three versions of this game (lol). From that experience, I'm sure that you can certainly get all the officer cards if you kept quit missions many times enough. For my 2nd and 3rd version, I've drawn the last officer card by quitting Nan Zhong Quest. It took less than 5 hours in both cases but maybe I was lucky, so I can't guarantee that you can do the same. Maybe it'll take more than 10 hours, but eventually you'll get the final card.
We are resting and saving ourselves to be bright - For the Jellicle Moon and the Jellicle Ball