I think Presence is a great modifying skill. Rather than have the GM change the difficulty of the roll based on Presence, ask to have Presence compliment your Resources roll.
But yeah, keeping track of passive skills is difficult as a GM, at least it is for me. I like to hope my players will call it out and make up for my failing in that area.
I tend to agree that exchange based rolls make social conflict feel unnatural and unwieldy. You've suggested a few time in our game the idea of using opposed rolls and consequential contests to decide the outcome and then just roleplay it in that direction. I like this idea, and used it a bit in the scene with Kai Bei and Yan Shi. I also like the purchase based rules that wyvern found, used when you are trying to get someone to do something.
See this link for the details of that method. I actually think that would have fit perfectly with the scene you are currently in with Fuling and Kai Bei.
You could probably break social conflicts down into two types, each covered by one of the two methods.
Opposed roles, extended contests, and consequential contests: You are trying to discover something (an interrogation, an interview, a few questions). You are trying to make someone react a certain way (become attracted to you, become angry). You are trying to make someone do something immediately (leave in embarrassment, come back to your place, hand over the keys to a vault). If you're doing an extended contest, consequential or otherwise, spacing the deciding rolls out allows players to make declarations and maneuvers to swing the conflict back and forth. This gives low social skills players at least a chance to succeed even if they are outmatched.
Purchase-based conflict: You want someone to behave in a particular way for a long period of time or to pursue a goal (back you politically, go and find an person/place/thing, guard a location while you are elsewhere).
I think these give a great deal of flexibility to players allowing them to roleplay their characters to the best of their ability and simply guide the scene to the decided result however fits the character. The more social skills you invest in, the more effective you'll be at approaching a wide variety of social conflicts. This also opens up justification for passive skills to become more active skills.