While I haven't had the opportunity to try it myself yet, Draw Steel's negotiation model seems to fit better. NPCs start with a certain amount of Patience (how long they're willing to put up with you) and Interest (how much they're willing to help you), as well as certain Motivations and Pitfalls (usually about 2 each, chosen from a common list of 12). Motivations are things the NPC cares about, and appealing to a Motivation will make the argument more effective, while Pitfalls are things the NPC actively dislikes or disdains and trying to appeal to that in an argument will make it automatically fail and lower the NPC's Interest. So a negotiation (and preparing for one) usually involves finding out what things make the NPC tick and then presenting arguments tailored to what you have learned. Usually, making an argument (successful or not) will lower the NPC's Patience – they have things to do, and can't be here talking to you all day, and if they hit 0 you're done. Hopefully the argument will also increase their Interest, which is measured on 0 to 5 where 0 to 2 are "No" with potential "and" or "but", and 3 to 5 are "Yes" with potential "but" or "and". I've seen it described as not so much being about changing the target's mind but about making the target realizing their interests and yours align.
The draw steel negotiation model is a formalization of how I've often conduct a negotiation over the years going back till at least the early 1990s. I like that model of encounter design and it's nice even from my perspective to see that encounter design laid out in a formal manner because it does help clarify what I'm doing when I decide after X attempts that the NPC can't be convinced any more.
The problem I have with it is precisely the problem you outlined with the 2D20 social rules, which is that while one particular encounter design for a social challenge might be well suited and congruent in that situation and a good way to run it, that's true only to the extent that a social challenge fits that design. For example, another common social challenge is you and someone else are having a debate, and you are both trying to convince a third party. And here, this might play out more like a combat, where taunts and insults might well sway the third party. Sure, the third party might have preferences related to their character as to what sort of arguments appeal or don't appeal to them, in as much as some third parties might fight find an ad hominem attack vulgar and reflect poorly on the speaker, while others might actually be looking for who can deliver the wittiest insult and embarrass their opponent the most as a fair deciding factor in which person to side with.
The point is that you have to tailor the social mechanics of your game to the situation involved just as you would tailor the combat resolution to the weapons and terrain. Singular "this is the one true way to run a social encounter" invariably force interactions into a model that is unrelated to how it actually would work in real life.
And the danger though I always find is the more you codify this as a system, the more you risk the problems you can get in codified abstract combat where the actual process of play at the table is something like, "I attack with my sword. 19 is a hit and that's 7 damage." That doesn't produce a transcript of play that allows for concrete visualization of the action. You need elements of the narration to reify the mechanics and ideally you want the narration to feed into resolution process and not the other way around.
So many of the attempts at social combat I've seen turn the exciting dialogue that you can produce at the table into, "I bring up the chancellor's missing daughter. That's a 19 hit and successful increase in interest, the Chancellor perks up and asks you to go on."
That's why I try not even to tell my players what is going on behind the scenes in my mind, because I want them interacting with the fiction and not the meta.