One thing that playing A Song of Ice and Fire helped me realise is that the purpose of social combat is basically to turn a socal encounter into a kind of set piece.
It's anti-climactic to try and convince the king that the threat of the Orcish invasion is real and then have it come down to one roll.
These days with D&D I tend to do it something like this: I write down a list of reasons why the king doesn't believe the Orcish Horde is real or doesn't want to act and give them a number rating. I also add in some facts about the king that can be leveraged.
eg
- Trusts his advisor 2 (who is a traitor assuring him the Orcish horde is not real.
- Cowardly 2 (Is afraid to lead his armies into the field)
- Concern for his kingdom 3
- Worried about his legacy 2
- Afraid of invasion by the neighbouring kingdom (worried that if he moves his armies north to fight the Orcs his neighbour will take the opportunity). 2
The PCs need to speak to the king and they need to hit at least 5 points. There's three points in concern for his kingdom but they can only get those points if they present three different arguments. Persuasion is not really necessary to make a lot of these points - they just have to make them. Persuasion is more for when they want to go against one of those points (convince him he can't trust his advisor) or when they contradict each other (allay his cowardice by appealling to how future generations will remember him) or try an approach not listed above but which is reasonably plausible. This means everyone can participate but characters with social skills just have a few more options.
I find this works quite well for common D&D situations where the players are trying to get something from an NPC. It provides just enough structure to communicate to the PCs. "He's wavering, but still doesn't look fully convinced".