Alright, here's what I've come up with:
Influence is removed in favor of the following skills:
Command (Cha): Giving orders and having them be followed effectively.
Deceive (Cha): Influencing other people's opinion by being less than truthful.
Empathy (Wis): Figuring out what other people are feeling, telling if they're lying, or trying to discover ulterior motives.
Intimidate (Str): Scaring people into doing what you want.
Negotiate (Cha): In addition to buying low, and selling high, it also covers trade deal and so on. Has some aspects of persuasion, but not exactly the same.
Persuade (Cha): Trying to convince people to switch to your point of view.
Mechanics
Roll your skill vs. the appropriate counterskill or save (Deceive vs. Empathy, Intimidate vs. Deceive, Negotiate vs. Negotiate, etc.), and if you win, then the target gets a bonus or penalty to a certain kind of actions. Probably just ±2 at a time, with boons and snags increasing the possible change from a single roll.
Also, I'm thinking of borrowing Passions from Reign and Runequest 6 and dividing them them into Influences, which arise from social rolls, and Passions that are chosen by the player based on some mechanic. Passions would be things like "Loyalty to the Duke +6" or "Hatred of Elves +2" or "Maintains Code of Honor +4," and then would function as a bonus on social rolls to advance the object of a Passion or a bonus on rolls to resist any attempt to create an Influence that's opposed to a Passion. So the guard with "Loyalty to the Duke +6" is going to be really hard to convince to look the other way while the players sneak into the Duke's private chambers.
Passions also act as buffers against negative Influences, so even if an Influence is successfully created, the target can ignore the mechanical penalties as long as they're equal to or less than the opposing Passion. I'll cap Influences and Passions at ±10, which prevents them from getting out of hand and lets someone set a Passion at +10 and have an unshakable conviction about something.
As for durations for Influences, I'm not sure. That's the kind of thing that will really need playtesting, I expect, which I currently haven't done any of.