Apology for length. Let me know if I understood you well, I shall change the answer as needed.
What do they want?
I must say I'm not entirely sure what is it that your group is after. Perhaps it's more about their own company than it is about the game? What they enjoy the most? Whom they want to play? What campaigns would they want? Are your GMs good in those areas?
Designing for others
May be surprisingly hard:
- requires lot of talking between designer and content-user (assuming they are different people)
- requires involvement of user (otherwise he'll often change the location / NPC to his liking on the spot, making the designer kinda offended: why did I spent so much time on it if he changed it in the end?)
- both points mean it requires time FROM both designers and users (note that GM == content user != player)
- collaborative writing tips that someone had already suggested here are a really fine idea!
- all the collaborative works of fiction I enjoyed had one supervisor / editor / master writer who had a final say in all, for conceptual integrity
Similar campaign from my own experience
I played a multi-GM campaign in the past, below are some details. In a nutshell, we had regional GMs and master one. We had our team of players and had lots of other characters (which we played occasionally, sometimes only once, sometimes more). There was a lot of world-building during and between the sessions.
Nominate master GM
One to rule them all, one to have decisive power over others. This unfortunate fellow will be the least likely to play but you will have conceptual integrity and all the discussions would have a final say.
Give areas of responsibility
This ties with veto power, as in "I'm responsible for this, it can't happen like you want it, since duke Archdragon would never allow it. However for this prince to get away X and Y would have to be at war or close to it, then their patrols would be lax on that road, or we may..."
Let folks have their areas, with pros and cons. Have a meeting where you would design those areas. Good example would be provinces of one country, where main GM would control the central province (royal or whatever that gives him the power over others). We had a province with strongest magical school but with LOTS of vampires, we had a scattered province (federation of counties) but with strong merchant guild, we had a province that had advanced technology (gunpowder) but had little farm lands and a province that could fed entire country and would have something left for export, but had weakest military (since they relied on some really old treaties that recently got broken twice).
Finding those strengths and weaknesses and discussing them made for a delightful world-building sessions between GMs.
Also, if other masters are flaky, having their own piece of world can motivate them.
Focus on crucial events
We had multiple characters: normal characters, and "VIP characters" that did politics and affected the game world. VIP characters could be different per session (ambassador here, master spy there, archmage and mage academy headmaster the next etc.) but they had usually power in our "regions".
So, for instance, I had one province where merchant guild was incredibly powerful and on VIP session I had an envoy who would bribe others, broke deals, proposed loans to other VIPs that later affected our usual PCs, since all of a sudden a poor province would start drafting people into military or would barricade a city that had a miner's guild that was inconvenient for my merchants but also happened to be a city where our PCs where staying.
We also could have fun with important regional events. One of GMs had a coup d'etat and wanted to see if this will actually work. So, he gave us characters and we had two assassins, master spy, brave guard and the prince himself. Coup failed but master spy lost his life, so province was shaken. Nice thinking on prince part to elevate brave guard to a hero for good publicity and to boost morale (and downplay death of master spy). Assassins managed to cover their tracks well enough that evidence of "who set it up" was weak at best.
This gives you power to play many different things which should boost attention of your very large group.
LARPs and battles
Simplify mechanics and play LARPs and perhaps battles (team-dependent). I firmly believe usual table-top RPG fails with so many players, unless from your group of ten less then 50% show up per session.
LARPs help with diplomatic events, battles with military campaigns. If your provinces have statistics (even as simple as: very good spy network, weak economy, mediocre military strength) then you can actually roll dice on how much information you get, how much income etc. Also, with battles you can mix battle mechanics in large-scale with role-playing cannon fodder during crucial moments.
This unfortunately means custom mechanics, but search some indies - I wouldn't be surprised if there are good solutions for rolling diplomacy, battle and or politics on a global scale.