Again, this underscores the reason for bombarding a city to near rubble before taking it. Also, did you switch every single laborer over to entertainers in the city. That seems to help with the flipping problem since there are no more unhappy laborers ready to culture flip.
I did take a couple of size 11 cities last game and it was against a civ whose citizens were unimpressed with my culture. There were an average of 6 resisters in the city. I move my red or low yellow units in to garrison, switch every single non resisting citizen to entertainers, and the resistance is crushed within 2 turns. Regent level.
Once the resistance is crushed, the city governor will resume production. Don't allow this to happen. There are still too many unhappy laborers. Keep them all as entertainers until the population drops another digit, otherwise the city will flip on you. Keep every unhappy laborer as an entertainer until you've taken surrounding cities. Once that happens, no longer have to worry about flipping.