I'm a forward person, so all of what I'll say now and in the future is not to be taken personally!

You're the GM Twilight, you should press the plot forward by making Kaede take the head of the group and go to the city, at least. That's what I been trying to do with my own character so far. Interaction between players is fine, but there's a fine line between that and a waste of time in game. If we stick too long at one spot most people will lose interest, including yourself (based on my previous experiences).

Maybe have a meeting with the PC in the Corporation and have a first fight after those who want it get the badge in town. 

The players don't exactly know what you want the plot to be so we can't really take the lead... :x
I'll drop this here knowing that you already have one, but if you need a (second) co-GM to discuss stuff about the plot ahead of time I'd be glad to help. 

^^'