I don't notice any difference in Culture - first policy is still 45, I've got quite an OP start with 6 tundra resources on my capital and upgraded them swiftly with god of all stars (some of those were ambers so they turned into 2C tiles), it's now 1000AD, I'm not in medieval and I didn't even start Piety yet. It's still bad in this regard, way too slow. I think a very severe policy/tech cost increase for each city and for base costs was way too much, especially when nobody wanted any of that. As it is, everyone has 5 policies, I have 6 despite an insane start + pantheon + Colosseum's bonus culture + Inspiration.
I think first policy was 50 pre-hotfix?
I am stopping a Japan game right now (due to being a bit tired of randomizing warmongering civs tbh, next 'random' will be a little less random) at 158 standard, 960 AD, so similar to your situation: beelined dojos and a level 4-5army; cotton provided some culture, but no city states to bully (only started ask tribute few turns ago during a peace treat break); 6 cities+2 puppets (and 2 razed, I think they raise policy cost forever?), 0 libraries, no own religion, growth is terrible and production godlike: I'm in Renaissance with 7 policies, the other guys (and my polinesian vassal) on my continent are at 5-6. Tbh I can't complain on standard speed, maybe epic is a bit off. I wouldn't use the cosmetic dates as a balancing factor anyway.
The Japan UA is providing some meaningful yields btw, and samurais haven't been the bulk of my forces yet.