That doesn't sound right. In BNW you must assign votes even if you have over the amount needed. If you have all the votes, then simply not vote and you won't win diplo while denying that from AIs.
Aside from that, I don't feel Diplo had too much of a change. The name of the game is still bribery.
I actually think Culture victory is easier now because you don't have to abandon Rationalism, even though the tree itself is nerfed (you should at least get Secularism anyways since you'll be running all those guild specialist on top of scientists). Now I think that all the victory conditions are more streamlined (you can switch midway more easily if things didn't go according to plan), except for perhaps Domination, but you can always start later with a tech lead.
Over 600 tourism per turn after Internet is a good number to shoot (if you got Intenational Game at this point it could even reach 1000), and tourism bomb the rest. If you're doing all those theming bonus with all the wonders possible on King and not achieve this number, then you're doing something wrong. Read Deau's Culture Guide. Also, play nice for the tourism multiplier (and so you can actually walk in and concert there).