Coming back from a long hiatus, and I could finish a game with 34UC Japan. I haven't yet given a feedback on a full game with the Kabuki, so here's how it has been in the last patch (VP 1.4.6, 34UC v75).
For context, the game itself was ripe for Kabuki to shine. I had two pleasant neighbors that kept showering their love for me by declaring joint wars about twice every single era, which kept my great work slots filled with the poetic rants of great generals from every generation imaginable. Plus, I got Great Wall, Brandenburg Gate and Glory of God reformation for extra UA procs. I also went for Tradition -> Artistry -> Industry -> Freedom to further push for great works and had a solid development all around, staying competitive all game and having those bonus trade routes from both Industry and Freedom for more Kabuki's internal TR culture procs. I ended the game at Modern Era with a cultural victory and 63 great works total.
The ITR culture procs are alright. With my ITRs revolving between 20 to 30 turns to complete, the culture given was about what I would gain in science and culture from an international TR to an allied CS or an advanced major civ, factoring in the scaling with era and the +% science/culture modifiers the latter can benefit from that Kabuki's procs can't (
e.g. golden age, Tradition's finisher). Overall, the culture proc isn't particularly powerful, it is more of not missing those important yields when resorting to internal TRs, nor having to engage in CS diplomacy in order to get them from TRs. With that yield difference factored out of international TRs, internal TRs are far more attractive: food and production tend to be more valuable than gold, more flexible for your city development's needs, you are safer from pillaging and it is very convenient for a non-diplomatic civ. I like that this aspect of the Kabuki pushes Japan to be an insular civilization, much like it was in history.
The unique guilds had weak starting procs, despite the good number of great works from earlier wars. They take time to build up to impactful values, as both great writers and artists have anemic bulbing at this point. Once you reach the later parts of the game, though, the Monogatari and Ukiyo-e guilds became impactful enough that I could slowly take the lead from a civ with bonuses to science and economy (Portugal, who was leading in both).
The Gagaku guild is notably weaker than the other two, though, since faith has already lost much of its importance by late Renaissance. The musician guild is also unlocked at the same tech as the Kabuki, rather than earlier, further delaying that faith beyond its prime. The faith from Gagaku was never particularly impactful, even in the lategame and despite having an unusually high amount of tourism with all those great works.
Overall, I think the unique guilds are interesting and scale well to the lategame, but are on the weaker side throughout the game's whole duration. The values do feel in the right spot in terms of fun and impact, and do round up the civ a bit, but they are a long term investment on a civ that is neither scientific nor diplomatic, meaning Japan doesn't profit from them as much as expected.
Of note is that it is hard to say that the Kabuki contributed towards the cultural victory. Science and gold helped indirectly, but isn't something you'd say that makes a civ like Portugal a potential cultural civ. The extra +2

on the guilds were of help, surely, but it is hard to tell that it was by much due to the frequent UA procs from the many generals I got. And the culture procs from TRs kinda goes against a cultural victory, as internal TRs don't get the tourism modifier of international TRs. Overall, I'd say that the Kabuki and its unique guilds go against the expectation of a stronger cultural victory for Japan.
As a whole, the Kabuki and its unique guilds are solid in terms of fun and themes, but leaning on the weak side due to its timing and mismatch with Japan's main victory paths.
As a suggestion, I think the unique guilds could each have two great work slots with a small theming bonus (+4 to +6) as their way to help with a cultural victory. Japan's UA faces diminishing returns at times due to not having enough theming buildings to allocate its works, which the unique guilds could address with this. Moreover, an early theming bonus for music would make the Gagaku guild relevant, as music theming is normally available only at Radio. This can round up the unique guilds' benefits towards the Renaissance and not risk major balance changes on the UB (in other words, not having to adjust the proc's percentages).