I propose a faction point based auction style election process. Here's how it works.
Let's say John Doe wants to be R6 (or even R7), then he signs himself up for the election ballot. From there, people have to be in a faction controlled region king of the hill style (like, you need to be within a certain area of a main zone of the map), which causes them to accumulate faction points. People deposit their faction points toward a certain candidate. Periodically, perhaps every month, the auction finalizes, and ties are decided randomly.
This rewards in game players and incentivizes inter-factional fights as well as taking new territories to generate even more faction points for control over the factions. It also frees up GM time and stories happen perfectly organically in the context of fighting over resources.
1. It still promotes popularity contests but with the additional bonus of being able to take a large group of players, jump to a faction and take it over with little issue.
2. Fighting between government factions (TDC/CPC) is probably something we don't want to encourage. Occasional civil wars are fine but repeated intra-factional conflicts between players that are generally meant to be more unified than the "clans" just to have a new leader I feel would be detrimental.
3. The "Clans" (including GOTC in this) seem to be aiming for a vastly different faction system than the other five. I'm not sure about FoE, but Syndicate want a family system which would allow for smaller groups of players to have interaction with their own "HC" (while that answers to the faction council) and GOTC has their cell system. Can't delete families and cells simply because they're small units and don't have the manpower to occupy zones when that might not be their niche.
4. I also don't think a king of the hill type thing fits corps either, not in a combat orientated way particularly due to the arguments previously prevented about not all factions just wearing different coloured clofhes and being pretty much exactly the same.
It might serve as a mechanic for one faction designed around it, but I don't think it's a good idea for all of them. Perhaps you could come up with some additional ideas around this and open it up for discussion/tweaking