I realize you stated you wish to sleep in Cozumel but in the past in low season when AA didn't have a return flight on my return day (Tuesday) or it was booked full I would take the 10:30 AM out of Cancun. I have left Cozumel on the first ferry and left the previous night and overnighted in downtown Cancun. Of the two, overnighting in Cancun seemed less stressful.
The Centro ADO bus station is a block and half up from city hall and two blocks from the very nice 'Artisan' park that is full of food vendors and often has concerts and activities (lots of families with kids so it's a safe area). Across the street from the bus terminal is a nice budget (2*) hotel, Hotel Caribe, with decent pool and restaurant, around $50 a night. Busses from Centro to the airport are frequent and cheap. It is a very relaxed way and you don't have to stress over construction delays between Playa and the airport. Last I heard Hiway 307 is being rebuilt due to the damage incurred hauling the materials for the Maya train project.