3step_paradise fits all those, save for the size- we're on the smaller end and slower pacing, but characters definitely have a heavy influence on things. The gods recently wiped the entire city clean after a major plot where the old ones pretty much go deposed, and characters are running everything. Players are pretty much allowed to come up with stuff for the city, plots, and even create the world outside the city walls. It's a jamjar, but it's a big jamjar that you can definitely influence.

Here's the link to our ad, if that sounds like something that might interest you!