snip/snip goes the previous chain for readability
Reading your post was a breath of fresh air. Fantastic to see someone who knows what they are talking about.
That being said, seeing as you are well informed, I'd be interested in what you think about using clever ways to circumvent how artificial these mechanics are. I've also been a GM for a long time and I very rarely offer more than one check and it's usually in the favor of the players because they've had extremely poor RNG at a very crucial moment and I'm not sure I've ever been in a game where the variance or standard deviation from the actual roll and the DC wasn't used to judge the gradient of success. Personally I think they should try to hide mechanics like this, such as by clever implementation of in game features.
For example, if you meet the criteria for a save in conversation if you could use the take ten rule of classic D&D then the game should treat it like an automatic success. This can also be used to circumvent incessant checks of almost any nature while making your build and specialization more important and requiring you to have a party with varied focus in specific skills. This is one of the instances in which I believe a 4 man party would actually work in their favor and be better than a 6 man party as you might not be able to fill every gap and still have to roll in certain circumstances where doing an automatic roll in the background when interacting with an object or choosing a specific dialogue choice that has only appeared because you've reached a certain skill threshold. I suggest all of this because every great GM I've ever seen has never told their players if they have succeeded or not keeping an air of uncertainty and extending the suspense. This would double to keep these mechanics out of your face and give you longer and more sustained 'free play' time without constantly shoving non diegetic features in your face all the time.
So there are several ways. Some of it has to do with context.
For instance; If I want to create a difficult negotiation challenge where the party has to get a powerful lord on their side to aid them in a controversial quest, I might implement a three-check "momentum" framework based on the following.
A. First, they have to come up with some way to get into his castle. This may involve sneaking past guards, negotiation an emergency meeting unannounced, or otherwise getting
access, which is more or less my encounter theme. I won't even bother setting up DCs or skills required/plausible until I've let my players at the problem-how they choose to approach to it is their own choice-but the idea is that they should require one check which, if successful, puts them in an advantageous position and which, if failed, puts them in a disadvantageous position.
B. Second, they have to come up with some way to actually arrange a meeting with the lord. If they've chosen to sneak in, they have to get past his bodyguards, who may have been alerted to intruders or whom are blissfully unaware. If they choose to go through official means via seeking an audience they have to convince his senechal or some other chief of staff. This requires a second check-failure makes the final check harder (because the lord will still hear them, just in very poor circumstances) and success makes it easy (the senechal greases the wheels, they pull some mysterious stranger shit where they materialize with dire omens in the middle of the night, whatever they are going for).
C. The money check. Actually pulling off their plan. However they've done it, they have to convince the lord to help (or otherwise secure his aid).
Now, the key here is to dynamically respond to the players actions and keep a goal-oriented encounter design. If they walk up to the front door and fail to convince the guards the senechal is awoken by extremely skeptical guards obviously ready to throw the PCs dungeon, instead of by earnest guards telling him about a vital message. If they convince the Senechal he immediately wakes the lord (or arranges an early morning meeting if this lord is cranky), while if they fail he has them show up during the lords typical court hours, meaning that they PC's have to fight an uphill battle in a public arena instead of a private one to get their controversial position through.
I might brainstorm some ideas, but otherwise let the players figure it out. The only core idea is that the PCs will likely face three layers of challenge requiring three checks, and each check impacts how the next one is made-advantage, disadvantage, or straight. Some ways of approaching the problem might be easier than others, some might have other side effects that come into play later (If the PCs manage to get thrown into the dungeon they might contract a disease while there, as a random idea), but that's how I'd structure it.
That's if I was designing a full encounter. If I suddenly decide I want to do this momentum system in the middle of a conversation-and I don't decide not to do it-I would rely on rebuttals to their arguments, thinking about a courtroom example-first they establish motive, then establish capacity, and finally prove X did it. In between each one the defense would step in and say something between "More than simply not wanting to kill Y, X wasn't even capable of it" to "Despite X's history with Y, he was incapable of killing him!" depending on how the previous check went.
But in general, I'd approach this system carefully. It works best with multiple actors or with multiple stages of conversation, rather than to convince a single person. Nettie should be a single check even under this system, and it does not work, organically, for everything.
The final thing to remember is that you don't need to fall in love with your own framework. I've had campaigns where I've set up damn similar encounters to the above, only for the wizard to pull out a scroll of dimension door I forgot I gave him, teleport into the lords chamber, pull out a scroll of modify memory I foolishly let him buy, and have the lord brainwashed in 30 seconds flat. It was ammoral as hell and cost him two consumables, and if ever discovered he's either dead or the campaign is now about fixing that problem, but he did it all with basically one check (by the lord, to resist modify memory). Which I was fine with, it was clever and in character, and I don't care if my encounter got bypass by gratuitous magic use.