Congrats on the win!
Must say there was no surprise in the win, but i enjoyed the way you did it, (although it was not what i suggested).
You played for fun, and it's fine. I pushed towards a more "commited" game, because of the learning stuff.
I think you give a bad example

to the youngsters here who will see you can win a game without focus on the victory condition.
A few thoughts are coming, but first my opinion on the next leader :
Napoleon is not well loved, but Louis is definitely hated. For the challenge, take Louis. Cultural? I don't think so, but we'll see.
Afterthoughts :
- you managed very well a late game cultural way, but you neglected some possibilities
1) 100% gold slider for a few turns)
2) not removing the cottages from London (not needing to press too hard on the culture to get to the goal) would have given you some more gold.
3) True the odds where high that you could get a GA in London. Bad luck? Not really. If you wanted loads of GA you should have gone for pacifism and 0 specialists in London while going for 10+ artists in coventry and hastings. Why? because +100% GPP from pacifism give only 50% more GPP in London, so you could have had more Great persons in coventry and hastings and much less in London.
I like to push one farm in front of the other by starving it for a few turns if i'm sure i'll get what i want there. Here you could have pushed coventry and hastings (not in the same time!) into starvation so that they pop a GA before London pops a prophet.
4) no hammers needed in the 3 big ones= no priest needed. Rush-buying!
Priests are welcome in guiness (ale must be appealing to those, don't you think?)
5) You could have rushed cathedral first, and used the overflow for the wonder (yes there is an overflow = all hammers you have in the city in one turn). This way, you could have built twice as much of the wonder in every turn you did build.
Turn 1 you start a cathedral
turn 2 you rush buy the cathedral
turn 3 you start a wonder + apply overflow.
Turn 4 you switch to another cathedral
turn 5 you buy the cathedral
turn 6 you build the wonder + apply overflow.
Just a general thought. Not very useful when you don't have any hammers going into the building. It's just a way to reduce the penalty for rushing wonders. More useful with pop rushing than with $-rushing.
What do you think of those unbuilt monasteries?
If you had built every monastery in London, you could have built missionaries there during the whole culture rushing time.
I'm sure coventry and hastings would have gained a lot from an early monastery too!