In your situation every turn that you can capture a city, containing a GW that adds a cultural building to every city, is counting, as this would add hundreds of cultural points each turn to your cultural score (belonging to the number of your cities). If you still have such a big amount of money, what is about trying to bribe a city as an invading place on another continent ? Additionally you could give a civ on another continent a new government and when that civ falls into Anarchy, those bribes would become even much cheaper. And there is another thought about bribing a city. If you conquer a city, every normal building providing culture is destroyed (and every SW, too). I´m not sure, if this also happens, when a city is gained by bribe.