Diplomatic victory isn't really diplomatic at all. It should just be referred to as "economic victory".
I like the idea of having to be world leader for a term and then deciding if it's ok. Of course, that present other challenges, in that everyone will immediately turn against you in order to prevent you from winning-it would create an inverse effect.
The problem with a diplomatic victory is that nobody will vote to lose the game. So the game shouldn't let any players decide-it should be entirely in the hand of city states to determine the winner, or some other factor that has no direct control-just influence.
I would suggest that the city states determine the diplomatic winner based on a totally new metric. The CS's would still track influence the current way, where you can purchase their loyalty and friendship through quests(but mostly money), but at the same time make it worthwhile to invest in them over the years. Keep a separate influence on each CS that tracks total influence that either doesn't degrade or degrades at a slower pace. For example, if you purchase 60 influence for 1000 gold, that adds 6 permanent influence.
The permanent influence is what primarily would motivate the CS voting systems. This grants city states a new role wherein they're real allies, not just purchased votes. When it comes time to vote for a world leader, the CS recognizes who has been their ally throughout history, not just the one who flashed cash two days before the vote.