I haven't had a chance to toss in my 2 gold before now due to the arrival of our new baby, but will try to squeeze in a few minutes now for that.
I like the idea of keeping all 6 leaders, and redistributing power. Ideally everyone who is elected should have roughly equal power, although that is unlikely in practice. We're trying to model splitting the brain of a single player into 9-20 parts, and certain sets of things like (tech rate and tech trading) and (happieness and lux trading) are inseparable.
Anyway, here are a few observations about effects I saw during DG3 which should be addressed here.
- Science chooses a tech queue, but there should be a strong interaction between what tech is researched and how high the slider is. This is really only an issue early in the game when a choice between min and max research is needed. How many civs we are in contact with is also a factor.
- Science needs to be linked with wonder building. We had two occurrances of choosing a research priority which rippled into wonder prebuilds not getting started, which meant that we didn't get the wonder.
- Under the system where the budget is owned by Domestic, often rushes are not requested, and in the case of my two terms as DL, I generally got an apathetic response when trying to discuss how the surplus should be used.
Making the senate responsible for the budget sounds appealing, as does ensuring that province size is held smaller. Also trying to make the provinces closer in production capability is a good idea. These ideas increase the chance that I'd be interested in being a governor.
An idea that I tossed out sometime in term 3 or 4 was the possibility of having the leader roles evolve as the game evolves.
For example, the relative importance of the Science Leader changes as the game progresses. The decisions of what to research and how much to spend on science are critical early, but as some have noted once we get to 4 or 5 turn research, there are few important choices left to be made.
Several people have suggested that the culture leader handle the cultural aspects of the forum in addition to those functions in the game. I'll also note that if we tried for a culture victory, then the CL would need to look at how early improvements and wonders can be built to achieve that victory type, while if we're going for another kind of victory the importance of that role diminishes.
That rambled a bit (baby interruptions

), so I'll toss something concrete in and see what happens.
The problem of balancing leader roles could be addressed by treating the 6 leaders as a council, with the President (or VP) holding a tie-breaking vote. Distribute the decision power for those items which span leader positions (science rate, science trades) by giving the council decision authority over those items.