You don't need to shut down the system to clean the stations, that should be happening all the time in a properly managed system. And when it comes to the train

You don't need to shut down the system to clean the stations, that should be happening all the time in a properly managed system. And when it comes to the trains themselves, with extra cars, you can easily rotate stock in and out in order to clean them, or have workers get on the trains at non-peak times (including at night) and clean as the train is in service. You don't need to deep clean each train every day to keep it clean, and with only 2 lines running 24/7, it's not like it'd be that hard to have extra rolling stock just for those two lines while cleaning the trains on non-24/7 lines at night. Simply put, 24/7 is not as big of an obstacle to cleanliness as you make it out to be. As other people mentioned, too, most of the work done in the evenings is track maintenance.