I have to say after this current game that its not worthwhile waiting for free speech if you have 1000 gold saved up and a nearby cultural city state. Just unlock the top two in Patronage and dump 1000 gold into the city state.
Also, I were easily capable of maintaining 50+

in this game, so all the turns I spent waiting without either piety or patronage were wasted as they could have produced extra culture with mandate of heaven (I had over 20

by the time I could have taken mandate of heaven, but waited for 1000 gold first instead).
The free speech / cristo redentor waits are far far weaker than keeping as many culture city states allied as possible, and creating as much excess

as you can for mandate of heaven. I'm at 1890 AD this time and just need two more polices, Im a long way away from Cristo Redentor, and am getting new policies every 11 turns.
The thing is that if you get wine or incense near your capital, lots of other luxuries, plus 3+ cultural city states, thats what you need to win this. It is fully dependant on getting as many cultural city states as possible, and as much excess

as you possibly can.