*chuckles* I can understand why the group struggles with cohesion, its not that there isn't a cohesive goal or a lack of a leader, infact theres more than one person with a leadership personality. Having none is bad for rp as no one guides along, but having .. I count four is an issue too, as all try to nudge the rp into a certain course of action, failing that struggle for dominance. Not unusual in big groups, but if none back down it is usually the wisest to split them up, if possible.
The fact of the matter is that any approach would work. Weiss', Xarkanas, Kats or Kieras, as the beauty of D&D is that a skilled DM can adjust the adventure to Good, Evil, Hackey Slashy or stealthy respectively, but the issue is that I've so far observed all of the leaders clashing, One pushes for diplomacy, one for preemptive strikes, one for direct confrontation and one for cautious approaches and all tug on the edges knotting the campaign together. It'd be best to reduce this to two leader types at best if none back down, for example, Weiss and Kat, with Weiss doing the talkies and Kat jumping in when it fails.
I can easily replace Xarkana with a less straight forwards leader type, I did pick her primarly because I though there would be a group cohesion problem for a lack of a leader, (though also because she as LE can easily stress-test a group), but unless something gives, focusing not exacerbating numbers would be the best sollution.