Looking back at my notes, I think the Feudal whipping had an effect, but also my wars happened earlier, so I had more cities to whip sooner. I had kicked Cleo off the continent by 110BC, whereas your first war hadn't started yet. In 10AD, I hit 1,001 culture, growing by 58cpt, and had completed my first 2 cathedrals (mid-GA). By 250AD, the GA was over, and I was just shy of 2,000 culture, but growing by 126cpt, with 15 cathedrals and a couple libraries. I declared on Carthage 2 turns later, and they were island-hopping by 410AD, whereas your Carthage war was again later. In 450AD, I had 50 cities, culture was 5,451, and growing by 229cpt. I had 21 cathedrals, most core cities had libraries, and I was in the process of whipping temples, and a couple quick cathedrals due to capturing ToA. It expired within about 10 turns, and most towns already had temples, so it wasn't a big factor, but I did get 2-3 cities to whip a cathedral before the temple.
The downside to all that is I never had near the population you did, so my production in Communism wasn't all that great. But by then, most easy culture was done, and I actually switched to Communism for the income (never thought I'd say that!). Maintenance was killing me, and recovering all that corrupted gold, multiplied by 60+ libraries and universities, would boost my research, giving me at least some chance to make some money off my 4-turn tech rivals on the other continent.