Add pet pal and persuasion to the party wide list please.
In SP the answer is to simply not have inter party disagreements and only having love/hate scores. Like in Bioware Dragon Age RPG's. They love/hate based on your decision, and leave if you make them hate you enough.
In MP, there should be no persuasion between characters. The dissenting (player who picks to not lift a finger) player always wins. You want to convince them, convince them in chat. That or those in agreement do and those not in agreement don't.
Persuasion should be a skill solely based on making NPC and non companion characters do things you want them to do. And in this case party wide is perfect. Because it's all about talking that dude in to giving you his amulet for a favor, and it doesn't matter if your silver tongues lizard companion throws in a couple of good arguments while your hashing it out.