some sort of figurehead?

Did the Kharim have some leader or significant person that lead them during this time?

I would say not until towards the very end of their wanderings.

My logic behind that is, since everyone lived in perfect harmony before the fall, most of the races probably did not understand the concept of mortal leadership. They were accustomed to the leadership of a divine being - but not from one of their own. As such, it would have taken a good while for them to figure out a decent system of organization - especially considering the constant pain they were in.

This opens the door to some crazy convoluted "politicking" at the end of the Exodus. As people are starting to grasp that a leader is necessary, confusion hits the fan. Different folks start grasping for power, and different groups backing each.

Y'all like?