I like this. I, too, think the envoy system is good, but it would be more fun if you had more influence on gaining envoys.
Maybe spies could work to reduce the envoys of another civ of your choosing?
My version of war support would be gifting units to a city-state and gain envoys in return. Generally speaking I think you should be able to gift units to city-states, I don't understand why they removed that.
However, I wouldn't make great people points able to buy envoys. Not sure about gold, either, it already plays a big part in the game, not sure I want even more reasons to build commercial districts and trade routes. That district thing sounds cool, though.