I improved to 1882, i believe 1850 is well possible, maybe even 1700s with a good map and pristine techpath/micro. I was still unlucky popping wrong great persons at ridicusly low odds.
The trick is to get to bio and NP fast without using scientist except for academy, that would allow you to grow a lot of GAs. Like i said, there is no point getting DP early, let alone PA. Keep bribing your future partner in free speech instead, while you research to radio. Radio is much more important than early PA, for the wonders unlocked and for era advancing which will increase the odds of partner running the culture slider. You should go PA when you hit radio and then drop research completely.
I found mansa and hatty really easy to get into culture mode once you PA, just make sure they research fission after you finished radio and also strip them of all the luxury resources, and gift them all the wonder/cathedral boosting resources they lack. The next turn they will drop the slider and won't be able to research fission in a million year, you go culture aswell and research something else, turning cottages into farms and building cathedrals.
Wonders to build:
1) oracle-->education (risky, getting CS is safer and would do almost as good)
2) oxford
3) NE
4) NP
5) Eiffel (if your partner doesn't start before you).
6) if you have marble, you can probably get sistine and taj.
To avoid too much GP pollution you should have at least 3 artist running all the time, so a playable start would be 8+ food surplus and some good commerce spot/ ( a combination of 6+ riverside grass/FP/gold/gem). Rest should be forest
I want to try a industrious partner now, ramsess/capac/luois and see. Since you bomb 3rd city the bottleneck is partner capital, and ind should have lot more wonders.